Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{3 x^{5}}{\left(1+x^{12}\right)} d x=?$ A. $\tan ^{-1} \mathrm{x}^{6}+\mathrm{C}$ B. $\frac{1}{4} \tan ^{-1} x^{6}+C$ C. $\frac{1}{2} \tan ^{-1} \mathrm{x}^{6}+\mathrm{C}$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{e^{x}}{\left(e^{2 x}+1\right)} d x=?$ A. $\cot ^{-1}\left(e^{x}\right)+C$ B. $\tan ^{-1}\left(e^{x}\right)+C$ C. $2 \tan ^{-1}\left(\mathrm{e}^{\mathrm{x}}\right)+\mathrm{C}$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\cos x}{\left(1+\sin ^{2} x\right)} d x=?$ A. $-\tan ^{-1}(\sin x)+C$ B. $\tan ^{-1}(\cos \mathrm{x})+\mathrm{C}$ C. $\tan ^{-1}(\sin x)+C$ D. $-\tan ^{-1}(\cos x)+C$ Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\sin x}{\left(1+\cos ^{2} x\right)} d x=?$ A. $-\tan ^{-1}(\cos \mathrm{X})+\mathrm{C}$ B. $\cot ^{-1}(\cos x)+C$ C. $-\cot ^{-1}(\cos \mathrm{x})+\mathrm{C}$ D. $\tan ^{-1}(\cos \mathrm{x})+\mathrm{C}$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{d x}{\left(9+4 x^{2}\right)} d x=?$ A. $\frac{1}{2} \tan ^{-1} \frac{2 \mathrm{x}}{3}+\mathrm{C}$ B. $\frac{1}{6} \tan ^{-1} \frac{2 \mathrm{x}}{3}+\mathrm{C}$ C. $\frac{1}{6} \tan ^{-1} \frac{3 x}{2}+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{d x}{\left(4+16 x^{2}\right)}=?$ A. $\frac{1}{32} \tan ^{-1} 4 \mathrm{x}+\mathrm{C}$ B. $\frac{1}{16} \tan ^{-1} \frac{x}{2}+C$ C. $\frac{1}{8} \tan ^{-1} 2 \mathrm{x}+\mathrm{C}$ D. $\frac{1}{4} \tan ^{-1} \frac{\mathrm{x}}{2}+\mathrm{C}$ Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{d x}{\left(9+x^{2}\right)}=?$ A. $\tan ^{-1} \frac{x}{3}+C$ B. $\frac{1}{3} \tan ^{-1} \frac{\mathrm{x}}{3}+\mathrm{C}$ C. $3 \tan ^{-1} \frac{x}{3}+C$ D. none of these Solution:...
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Question: Evaluate: $\int \frac{d x}{\sqrt{4 x^{2}-25}}$ Solution:...
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Question: Evaluate: $\int \frac{d x}{\sqrt{4-9 x^{2}}}$ Solution:...
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Question: Evaluate: $\int \frac{\mathrm{dx}}{\sqrt{9 \mathrm{x}^{2}+16}}$ Solution:...
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Question: Evaluate: $\int(2 x+1)\left(\sqrt{x^{2}+x+1}\right) d x$ Solution:...
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Question: Evaluate: $\int \frac{\sec ^{2}(\log x)}{x} d x$ Solution:...
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Question: Evaluate: $\int \frac{(1+\tan x)}{(x+\log \sec x)} d x$ Solution:...
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Question: Evaluate: $\int \frac{d x}{(\sqrt{x+2}+\sqrt{x+1})}$ Solution:...
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Question: Evaluate: $\int \frac{\sec ^{2} x}{\operatorname{cosec}^{2} x} d x$ Solution:...
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Question: Evaluate: $\int \frac{\cot x}{\sqrt{\sin x}} d x$ Solution:...
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Question: Evaluate: $\int e^{x}\{\tan x-\log \cos x\} d x$ Solution:...
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Question: Evaluate: $\int \frac{x e^{x}}{(x+1)^{2}} d x$ Solution:...
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