Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\sin \sqrt{x}}{\sqrt{x}} d x=?$ A. $2 \cos \sqrt{x}+C$ B. $-2 \cos \sqrt{\mathrm{x}}+\mathrm{C}$ C. $-\frac{\cos \sqrt{x}}{2}+C$ D. $\frac{\cos \sqrt{x}}{2}+C$ 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: $\int \frac{e^{\tan ^{-1} x}}{\left(1+x^{2}\right)} d x=?$ A. $\frac{e^{\tan ^{-1} x}}{x}+C$ B. $e^{\tan ^{-1} x}+C$ C. $e^{x} \tan ^{-1} x+C$ 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: $\int \frac{e^{\sqrt{x}}}{\sqrt{x}} d x=?$ A. $\mathrm{e}^{\sqrt{x}}+C$ B. $\frac{1}{2} \mathrm{e}^{\sqrt{x}}+C$ C. $2 \mathrm{e}^{\sqrt{x}}+C$ 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: $\int e^{x^{3}} x^{2} d x=?$ A. $e^{x^{3}}+C$ B. $\frac{1}{3} e^{x^{3}}+C$ C. $\frac{1}{6} e^{x^{3}}+C$ 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: $\int \frac{1}{x(\log x)} d x=?$ A. $\log |\mathrm{X}|+\mathrm{C}$ B. $\frac{-2}{\mathrm{x}^{2}}+\mathrm{C}$ C. $(\log x)^{2}+C$ D. $\log |\log x|+C$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\sec ^{2}(\log x)}{x} d x=?$ A. $\log (\tan x)+C$ B. $-\log (\tan x)+C$ C. $\tan (\tan x)+C$ D. $-\tan (\log x)+C$ 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: $\int \frac{\log x}{x} d x=?$ A. $\frac{1}{2}(\log x)^{2}+C$ B. $-\frac{1}{2}(\log x)^{2}+C$ C. $\frac{2}{x^{2}}+C$ D. $\frac{-2}{x^{2}}+C$ 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: $\int \sin ^{3} x d x=?$ A. $-\frac{3}{4} \cos x+\frac{\cos 3 x}{12}+C$ B. $\frac{3}{4} \cos x+\frac{\cos 3 x}{12}+C$ C. $-\frac{3}{4} \cos x-\frac{\cos 3 x}{12}+C$ 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: $\int \sqrt{1+\sin x} d x=?$ A. $-\sqrt{2} \sin \left(\frac{\pi}{4}-\frac{x}{2}\right)+C$ B. $\sqrt{2} \sin \left(\frac{\pi}{4}-\frac{x}{2}\right)+C$ C. $-2 \sqrt{2} \sin \left(\frac{\pi}{4}-\frac{x}{2}\right)+C$ 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: $\int \sqrt{1-\cos x} d x=?$ A. $-\sqrt{2} \cos \frac{x}{2}+C$ B. $-2 \sqrt{2} \cos \frac{x}{2}+C$ C. $\frac{-1}{2} \cos \frac{x}{2}+C$ D. $\frac{-1}{\sqrt{2}} \cos \frac{x}{2}+C$ Solution: where $\mathrm{c}$ is the integrating constant....
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \tan ^{2} \frac{\mathrm{x}}{2} \mathrm{dx}=?$ A. $\tan \frac{x}{2}-x+C$ B. $\tan \frac{x}{2}+x+C$ C. $2 \tan \frac{x}{2}+x+C$ D. $2 \tan \frac{x}{2}-x+C$ 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: $\int e^{(3 x+4)} d x=?$ A. $\frac{3}{(\log 2)} \cdot 2^{(3 x+4)}+C$ B. $\frac{2^{(3 x+4)}}{3(\log 2)+C}$ C. $\frac{2^{(3 x+4)}}{2(\log 3)}+C$ 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: $\int e^{(5-3 x)} d x=?$ A. $-3 \mathrm{e}^{(5-3 \mathrm{x})}+\mathrm{C}$ B. $\frac{1}{3} e^{(5-3 x)}+C$ C. $\frac{e^{(5-3 x)}}{-3}+C$ 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: $\int \cos 3 x d x=?$ A. $-\frac{1}{3} \sin 3 x+C$ B. $\frac{1}{3} \sin 3 x+C$ C. $3 \sin 3 x+C$ D. $-3 \sin 3 x+c$ 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: $\int \sec ^{2}(7-4 x) d x=?$ A. $\frac{1}{4} \tan (7-4 x)+C$ B. $\frac{-1}{4} \tan (7-4 x)+C$ C. $4 \tan (7-4 x)+C$ D. $-4 \tan (7-4 x)+C$ 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: $\int \sqrt{a x+b} d x=?$ A. $\frac{2(a x+b)^{3 / 2}}{3 a}+C$ B. $\frac{3(a x+b)^{3 / 2}}{2 a}+C$ C. $\frac{1}{2 \sqrt{a x+b}}+C$ 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: $\int \frac{1}{(2-3 x)^{4}} d x=?$ A. $\frac{1}{15(2-3 x)^{5}}+C$ B. $\frac{1}{-12(2-3 x)^{3}}+C$ C. $\frac{1}{9(2-3 x)^{3}}+C$ 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: $\int(3-5 x)^{7} d x=?$ A. $-5(3-5 x)^{6}+C$ B. $\frac{(3-5 x)^{8}}{-40}+C$ C. $\frac{-5(3-5 x)^{8}}{8}+C$ 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: $\int(2 \mathrm{x}+3)^{5} \mathrm{dx}=?$ A. $\frac{(2 x+3)^{6}}{6}+C$ B. $\frac{(2 x+3)^{4}}{8}+C$ C. $\frac{(2 x+3)^{6}}{12}+C$ D. none of these Solution:...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{(\sin x+\cos x)}{\sqrt{\sin 2 x}} d x$ Solution:...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\left(x^{2}+1\right)}{\left(x^{4}+1\right)} d x$ Solution:...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{2 x \tan ^{-1} x^{2}}{\left(1+x^{4}\right)} d x$ Solution:...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int\left(\sin ^{-1} x\right)^{2} d x$ Solution:...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\mathrm{dx}}{\left(\mathrm{x}^{1 / 2}+\mathrm{x}^{1 / 3}\right)}$ Solution:...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\sin \left(2 \tan ^{-1} x\right)}{\left(1+x^{2}\right)} d x$ Solution:...
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