Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int e^{x}(\tan x+\log \sec x) d x=?$ A. $e^{x} \log \sec x+C$ B. $e^{x} \tan x+c$ C. $e^{x}(\log \cos x)+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int e^{x}\left\{\sin ^{-1} x+\frac{1}{\sqrt{1-x^{2}}}\right\} d x=?$ A. $e^{x} \cdot \frac{1}{\sqrt{1-x^{2}}}+C$ B. $e^{x} \sin ^{-1} x+C$ C. $\frac{-\mathrm{e}^{\mathrm{x}}}{\sin ^{-1} \mathrm{x}}+\mathrm{C}$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int e^{x}\left(\frac{1}{x^{2}}-\frac{2}{x^{3}}\right) d x=?$ A. $\frac{-e^{x}}{x^{2}}+C$ $B$ $\frac{e^{x}}{x^{2}}+C$ C. $\mathrm{e}^{\mathrm{x}}\left(\frac{-1}{\mathrm{x}}+\frac{1}{\mathrm{x}^{2}}\right)+\mathrm{C}$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \mathrm{e}^{\mathrm{x}}\left\{\frac{1}{\mathrm{x}}-\frac{1}{\mathrm{x}^{2}}\right\} \mathrm{dx}=?$ A. $e^{x}\left\{\log x+\frac{1}{x}\right\}+C$ B. $x e^{x}-e^{x}+C$ C. $\mathrm{e}^{\mathrm{x}} \cdot \frac{1}{\mathrm{x}}+\mathrm{C}$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int\left(\sin ^{-1} x\right)^{2} d x=?$ A. $\frac{2 \sin ^{-1} x}{\sqrt{1-x^{2}}}+C$ B. $\frac{1}{3}\left(\sin ^{-1} x\right)^{3}+\frac{1}{\sqrt{1-x^{2}}}+C$ C. $x\left(\sin ^{-1} x\right)^{2}+\left(\sin ^{-1} x\right) \sqrt{1-x^{2}}+2 x+C$ D. $x\left(\sin ^{-1} x\right)^{2}+2\left(\sin ^{-1} x\right) \sqrt{1-x^{2}}-2 x+C$ Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sin (\log x) d x=?$ A. $\frac{1}{2} x \sin \log x+\frac{1}{2} x \cos (\log x)+C$ B. $\frac{1}{2} x \sin \log x-\frac{1}{2} x \cos (\log x)+C$ C. $-\frac{1}{2} x \sin \log x+\frac{1}{2} x \cos (\log x)+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int x \tan ^{-1} x d x=?$ A. $\frac{1}{2}\left(x^{2}+1\right) \tan ^{-1} x-\frac{1}{2} x+C$ B. $\frac{1}{2}\left(x^{2}-1\right) \tan ^{-1} x-\frac{1}{2} x+C$ C. $\frac{1}{2}\left(x^{2}+1\right) \tan ^{-1} x+\frac{1}{2} x+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) d x=?$ A. $2 x \tan ^{-1} x+\log \left(1+x^{2}\right)+C$ B. $-2 x \tan ^{-1} x-2 \log \left(1+x^{2}\right)+C$ C. $2 x \tan ^{-1} x-\log \left(1+x^{2}\right)+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int x^{3} \cos x^{2} d x=?$ A. $x^{2} \sin x^{2}+\cos x^{2}+C$ B. $\frac{1}{2} x^{2} \sin x^{2}+\frac{1}{2} \cos x^{2}+C$ C. $-\frac{1}{2} x^{2} \sin x^{2}+\frac{1}{2} \cos x^{2}+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int x \sin x \cos x d x=?$ A. $-\frac{1}{4} x \cos 2 x+\frac{1}{8} \sin 2 x+C$ B. $\frac{1}{4} x \cos 2 x+\frac{1}{8} \sin 2 x+C$ C. $\frac{1}{4} x \cos 2 x-\frac{1}{8} \sin 2 x+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sin x \log (\cos x) d x=?$ A. $\cos x \log (\cos x)-\cos x+C$ B. $-\cos x \log (\cos x)+\cos x+C$ C. $\cos x \log (\cos x)+\cos x+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int x^{2} \cos x d x=?$ A. $x^{2} \sin x+2 x \cos x-2 \sin x+C$ B. $2 x \cos x-x \sin x+2 \sin x+C$ C. $x^{2} \sin x-2 x \sin x+2 \sin x+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \tan ^{-1}\left(\frac{3 x-x^{3}}{1-3 x^{2}}\right) d x=?$ A. $3 x \tan ^{-1} x+\frac{3}{2} \log \left(1+x^{2}\right)+C$ B. $3 x \tan ^{-1} x-\frac{3}{2} \log \left(1+x^{2}\right)+C$ C. $3 x \cos ^{-1} x-\frac{3}{2} \sqrt{1-x^{2}}+C$ D. $3 x \sin ^{-1} x+\frac{3}{2} \sqrt{1-x^{2}}+C$ Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \tan ^{-1} \sqrt{\frac{1-x}{1+x}} d x=?$ A. $\frac{1}{2} x\left(\cos ^{-1} x\right)+\frac{1}{2} \sqrt{1-x^{2}}+C$ B. $\frac{1}{2} \mathrm{x}\left(\sin ^{-1} \mathrm{x}\right)+\frac{1}{2} \sqrt{1-\mathrm{x}^{2}}+\mathrm{C}$ C. $\frac{1}{2} x\left(\cos ^{-1} x\right)-\frac{1}{2} \sqrt{1-x^{2}}+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x=?$ A. $2 x \tan ^{-1} x+\log \left|1+x^{2}\right|+C$ B. $2 x \tan ^{-1} x-\log \left|1+x^{2}\right|+C$ C. $2 x \sin ^{-1} x+\log \left|1+x^{2}\right|+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sin ^{-1}\left(3 x-4 x^{3}\right) d x=?$ A. $3\left[x \sin ^{-1} x+\sqrt{1-x^{2}}\right]+C$ B. $3\left[x \sin ^{-1} x-\sqrt{1-x^{2}}\right]+C$ C. $\frac{3 x^{2}}{2}+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \sec ^{-1} x d x=?$ A. $x \sec ^{-1} x+\log \left|x+\sqrt{x^{2}-1}\right|+C$ B. $x \sec ^{-1} x-\log \left|x+\sqrt{x^{2}-1}\right|+C$ C. $x \sec ^{-1} x+\log \left|x-\sqrt{x^{2}-1}\right|+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \tan ^{-1} x d x=?$ A. $x \tan ^{-1} \mathrm{x}+\frac{1}{2} \log \left|1+\mathrm{x}^{2}\right|+\mathrm{C}$ B. $x \tan ^{-1} x-\frac{1}{2} \log \left|1+x^{2}\right|+C$ C. $-x \tan ^{-1} x+\frac{1}{2} \log \left|1+x^{2}\right|+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \cos ^{-1} \mathrm{x} d \mathrm{x}=?$ A. $x \cos ^{-1} x-\sqrt{1-x^{2}}+C$ B. $x \cos ^{-1} x+\sqrt{1-x^{2}}+C$ C. $x \sin ^{-1} x-\sqrt{1-x^{2}}+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \tan ^{-1} \sqrt{\mathrm{x}} \mathrm{dx}=?$ A. $(x-1) \tan ^{-1} \sqrt{x}+\sqrt{x}+C$ B. $(x+1) \tan ^{-1} \sqrt{x}-\sqrt{x}+C$ C. $\frac{1}{2} \sqrt{x} \tan ^{-1} \sqrt{x}-\frac{1}{2} \sqrt{x}+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int x \tan ^{-1} x d x=?$ A. $\frac{1}{2} \tan ^{-1} x+\log \left(1+x^{2}\right)-\frac{1}{2} x+C$ B. $\frac{1}{2} x^{2} \tan ^{-1} x+\frac{1}{2} x+C$ C. $\frac{1}{2}\left(1+x^{2}\right) \tan ^{-1} x-\frac{1}{2} x+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{x \tan ^{-1} x}{\left(1-x^{2}\right)^{3 / 2}} d x=?$ A. $\frac{\tan ^{-1} x}{\sqrt{1+x^{2}}}-\frac{x}{\sqrt{1+x^{2}}}+C$ B. $\frac{-\tan ^{-1} x}{\sqrt{1+x^{2}}}+\frac{x}{\sqrt{1+x^{2}}}+C$ C. $\frac{x \tan ^{-1} x}{\sqrt{1+x^{2}}}+\frac{1}{2} \log \left|\frac{x}{\sqrt{1+x^{2}}}\right|+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\sin ^{-1} x}{\left(1-x^{2}\right)^{3 / 2}} d x=?$ A. $\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}-\frac{1}{2} \log \left|1-x^{2}\right|+C$ B. $x \sin ^{-1} x+\frac{1}{2} \log \left|1-x^{2}\right|+C$ C. $\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}+\frac{1}{2} \log \left|1-x^{2}\right|+C$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int e^{\sin x} \sin 2 x d x=?$ A. $(2 \sin x) e^{\sin x}+C$ B. $(2 \cos x) e^{\sin x}+C$ C. $2 e^{\sin x}(\sin x+1)+C$ D. $2 e^{\sin x}(\sin x-1)+C$ Solution: To find: Value of $\int e^{\sin x} \sin 2 x d x$...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sin \sqrt{x} d x=?$ A. $-\sqrt{x} \cos \sqrt{x}+C$ B. $-\sqrt{x} \cos \sqrt{x}-2 \sin \sqrt{x}-C$ C. $-2 \sqrt{x} \cos \sqrt{x}+2 \sin \sqrt{x}-C$ D. none of these Solution:...
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