Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sin ^{3} x \cos ^{3} x d x=?$ A. $-\frac{1}{4} \cos ^{4} \mathrm{x}+\frac{1}{6} \cos ^{6} \mathrm{x}+\mathrm{C}$ B. $\frac{1}{4} \cos ^{4} x-\frac{1}{6} \cos ^{6} x+C$ C. $\frac{1}{4} \cos ^{4} x+\frac{1}{6} \cos ^{6} x+C$ 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: $\int \tan ^{5} x d x=?$ A. $\frac{1}{6} \tan ^{6} \mathrm{x}+\mathrm{C}$ B. $\frac{1}{4} \tan ^{4} x+\frac{1}{2} \tan ^{2} x+\log |\sec x|+C$ C. $\frac{1}{4} \tan ^{4} x-\frac{1}{2} \tan ^{2} x+\log |\sec x|+C$ 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: $\int \sec ^{5} x \tan x d x=?$ A. $\frac{1}{5} \tan ^{5} x+C$ B. $\frac{1}{5} \sec ^{5} \mathrm{x}+\mathrm{C}$ C. $5 \log |\cos x|+C$ 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: $\int \frac{\sin ^{6} x}{\cos ^{8}} d x=?$ A. $\frac{1}{7} \tan ^{7} \mathrm{x}+\mathrm{C}$ B. $\frac{1}{7} \sec ^{7} \mathrm{x}+\mathrm{C}$ C. $\log \left|\cos ^{6} x\right|+C$ 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: $\int \frac{\left(x^{2}+1\right)}{\left(x^{4}+1\right)} d x=?$ A. $\frac{1}{\sqrt{2}} \tan ^{-1}\left(\mathrm{x}-\frac{1}{\mathrm{x}}\right)+\mathrm{C}$ B. $\frac{1}{\sqrt{2}} \cot ^{-1}\left\{\left(x-\frac{1}{x}\right)\right\}+C$ C. $\frac{1}{\sqrt{2}} \tan ^{-1}\left\{\frac{1}{\sqrt{2}}\left(x-\frac{1}{x}\right)\right\}+C$ 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: $\int \frac{\sec ^{2} x}{\sqrt{1-\tan ^{2} x}} d x=?$ A. $\sin ^{-1}(\tan x)+C$ B. $\cos ^{-1}(\sin x)+C$ C. $\tan -1(\cos x)+C$ D. $\tan ^{-1}(\sin x)+C$ 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: $\int \frac{\mathrm{dx}}{(1-\cot x)}=?$ A. $\log |\sin x-\cos x|+C$ B. $\frac{1}{2} \log |\sin x-\cos x|+C$ C. $\frac{1}{2} x-\frac{1}{2} \log |\sin x-\cos x|+C$ D. $\frac{1}{2} x+\frac{1}{2} \log |\sin x-\cos x|+C$ 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: $\int \frac{d x}{(1-\tan x)}=?$ A. $\frac{1}{2} \log |\sin x-\cos x|+C$ B. $\frac{1}{2} x+\frac{1}{2} \log |\sin x-\cos x|+C$ C. $\frac{1}{2} x-\frac{1}{2} \log |\sin x-\cos x|+C$ 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: $\int \frac{\sin x}{(\sin x-\cos x)} d x=?$ A. $\frac{1}{2} x-\frac{1}{2} \log |\sin x-\cos x|+C$ B. $\frac{1}{2} x+\frac{1}{2} \log |\sin x-\cos x|+C$ C. $\log |\sin x-\cos x|+C$ 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: $\int \sqrt{e^{x}-1} d x$ A. $\frac{3}{2}\left(e^{x}-1\right)^{3 / 2}+C$ B. $\frac{1}{2}\left(e^{x}-1\right)^{1 / 2}+C$ C. $\frac{2}{3}\left(e^{x}-1\right)^{3 / 2}+C$ 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: $\int \frac{\mathrm{dx}}{(1+\sqrt{\mathrm{x}})}=?$ A. $\sqrt{\mathrm{x}}-\log |1+\sqrt{\mathrm{x}}|+\mathrm{C}$ B. $\sqrt{\mathrm{x}}+\log |1+\sqrt{\mathrm{x}}|+\mathrm{C}$ C. $2 \sqrt{x}-2 \log |1+\sqrt{x}|+C$ 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: $\int x \sqrt{x^{2}-x} d x=?$ A. $\frac{1}{3}\left(x^{2}-1\right)^{3 / 2}+C$ B. $\frac{2}{3}\left(x^{2}-1\right)^{3 / 2}+C$ C. $\frac{1}{\sqrt{\mathrm{x}^{2}-1}}+\mathrm{C}$ 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: $\int x \sqrt{x-1} d x=?$ A. $\frac{2}{3}(x-1)^{3 / 2}+C$ B. $\frac{2}{5}(x-1)^{5 / 2}+C$ C. $\frac{2}{5}(x-1)^{5 / 2}+\frac{3}{2}(x-1)^{3 / 2}+C$ 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: $\int \frac{1}{x \sqrt{x^{4}-1}} d x=?$ A. $\sec ^{-1} x^{2}+C$ B. $\frac{1}{2} \sec ^{-1} x^{2}+C$ C. $\operatorname{cosec}^{-1} x^{2}+C$ 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: $\int \frac{(x+1) e^{x}}{\cos ^{2}\left(x e^{x}\right)} d x=?$ A. $\tan \left(x e^{x}\right)+C$ B. $-\tan \left(x e^{x}\right)+C$ C. $\cot \left(x e^{x}\right)+C$ 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: $\int x^{2} \sin x^{3} d x=?$ A. $\cos x^{3}+C$ B. $-\cos x^{3}+C$ C. $-\frac{1}{3} \cos x^{3}+C$ 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: $\int \frac{e^{\sqrt{x}} \cos \left(e^{\sqrt{x}}\right)}{\sqrt{x}} d x=?$ A. $\sin \left(e^{\sqrt{x}}\right)+C$ B. $\frac{1}{2} \sin \left(e^{\sqrt{x}}\right)+C$ C. $2 \sin \left(e^{\sqrt{x}}\right)+C$ 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: $\int x \sin ^{3} x^{2} \cos x^{2} d x=?$ A. $\frac{1}{4} \sin ^{4} x^{2}+C$ B. $\frac{1}{8} \sin ^{4} x^{2}+C$ C. $\frac{1}{2} \sin ^{4} x^{2}+C$ 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: $\int e^{\cos ^{2} x} \sin 2 x d x=?$ A. $e^{\cos ^{2} x}+C$ B. $-e^{\cos ^{2} x}+C$ C. $e^{\sin ^{2} x}+C$ 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: $\int e^{\tan x} \sec ^{2} x d x=?$ A. $e^{\tan x}+\tan x+C$ B. $e^{\tan x} \cdot \tan x+C$ C. $e^{\tan x}+C$ 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: $\int e^{(5-3 x)} d x=?$ A. $\frac{3^{(5-3 x)}}{3(\log 3)}+C$ B. $\frac{3^{(4-3 x)}}{(\log 3)}+C$ C. $-3^{(5-3 x)} \log 3+C$ 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: $\int x \sqrt{x^{2}-1} d x=?$ A. $\frac{2}{3}\left(x^{2}-1\right)^{3 / 2}+C$ B. $\frac{1}{3}\left(x^{2}-1\right)^{3 / 2}+C$ C. $\frac{1}{\sqrt{\mathrm{x}^{2}-1}}+\mathrm{C}$ 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: $\int \frac{\mathrm{dx}}{(2-3 \mathrm{x})}=?$ A. $-3 \log |2-3 x|+C$ B. $-\frac{1}{3} \log |2-3 x|+C$ C. $-\log |2-3 x|+C$ 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: $\int \frac{2 x \tan ^{-1} x^{2}}{\left(1+x^{4}\right)} d x=?$ A. $\left(\tan ^{-1} x^{2}\right)^{2}+C$ B. $2 \tan ^{-1} x^{2}+C$ C. $\frac{1}{2}\left(\tan ^{-1} x^{2}\right)^{2}+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{(x+1)(x+\log x)^{2}}{x} d x=?$ A. $\frac{1}{3}(x+\log x)^{3}+C$ B. $\frac{x^{2}}{2}+x+C$ C. $\frac{x^{3}}{3}+\frac{x^{2}}{2}+x+C$ D. none of these Solution:...
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