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Question: Evaluate: $\int_{0}^{\pi / 6} \sec ^{2} x d x$ Solution:...
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Question: Evaluate: $\int_{0}^{1} \frac{d x}{\sqrt{1-x^{2}}}$ Solution:...
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Question: Evaluate: $\int_{0}^{\infty} \frac{d x}{\left(1+x^{2}\right)}$ Solution:...
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Question: Evaluate: $\int_{0}^{1} \frac{d x}{\left(1+x^{2}\right)}$ Solution:...
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Question: Evaluate: $\int_{1}^{8} \frac{d x}{x^{\frac{3}{3}}}$ Solution:...
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Question: Evaluate: $\int_{0}^{1} \frac{d x}{\sqrt[3]{x}}$ Solution:...
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Question: Evaluate: $\int_{1}^{4} \frac{d x}{\sqrt{x}}$ Solution:...
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Question: Evaluate: $\int_{0}^{16} x \frac{\pi}{4} d x$ Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\sqrt{16+(\log x)^{2}}}{x} d x=?$ A. $\frac{1}{2} \log x \cdot \sqrt{16+(\log x)^{2}}+8 \log \left|\log x+\sqrt{16+(\log x)^{2}}\right|+C$ B. $\frac{1}{2} \log x \cdot \sqrt{16+(\log x)^{2}}+4 \log \left|\log x+\sqrt{16+(\log x)^{2}}\right|+C$ C. $\log x \cdot \sqrt{16+(\log x)^{2}}+16 \log \left|\log x+\sqrt{16+(\log x)^{2}}\right|+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int e^{x} \sqrt{e^{2 x}+4} d x=?$ A. $\frac{1}{2} e^{x} \sqrt{e^{2 x}+4}-2 \log \left|e^{x}+\sqrt{e^{2 x}+4}\right|+C$ B. $\frac{1}{2} e^{x} \sqrt{e^{2 x}+4}+2 \log \left|e^{x}+\sqrt{e^{2 x}+4}\right|+C$ C. $e^{x} \sqrt{e^{2 x}+4}+\frac{1}{2} \log \left|e^{x}+\sqrt{e^{2 x}+4}\right|+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sqrt{9 x^{2}+16} d x=?$ A. $\frac{x}{2} \sqrt{9 x^{2}+16}+\frac{8}{3} \log \left|3 x+\sqrt{9 x^{2}+16}\right|+C$ B. $\frac{x}{2} \sqrt{9 x^{2}+16}-\frac{8}{3} \log \left|3 x+\sqrt{9 x^{2}+16}\right|+C$ C. $x \sqrt{9 x^{2}+16}+24 \log \left|3 x+\sqrt{9 x^{2}+16}\right|+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sqrt{x^{2}-4 x+2} d x=?$ A. $\frac{1}{2}(x-2) \sqrt{x^{2}-4 x+2}+\log \left|(x-2)+\sqrt{x^{2}-4 x+2}\right|+C$ B. $(x-2) \sqrt{x^{2}-4 x+2}+\frac{1}{2} \log \left|(x-2)+\sqrt{x^{2}-4 x+2}\right|+C$ C. $\frac{1}{2}(x-2) \sqrt{x^{2}-4 x+2}-\log \left|(x-2)+\sqrt{x^{2}-4 x+2}\right|+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sqrt{x^{2}-16} d x=?$ A. $x \sqrt{x^{2}-16}-4 \log \left|x+\sqrt{x^{2}-16}\right|+C$ B. $\frac{x}{2} \sqrt{x^{2}-16}-8 \log \left|x+\sqrt{x^{2}-16}\right|+C$ C. $\frac{x}{2} \sqrt{x^{2}-16}+8 \log \left|x+\sqrt{x^{2}-16}\right|+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \cos x \sqrt{9-\sin ^{2} x} d x=?$ A. $\frac{1}{2} \sin x \sqrt{9-\sin ^{2} x}+\frac{9}{2} \sin ^{-1}\left(\frac{\sin x}{3}\right)+C$ B. $\frac{\sin x}{2} \sqrt{9-\sin ^{2} x}+\frac{9}{2} \sin ^{-1}\left(\frac{\sin x}{3}\right)+C$ C. $\frac{1}{2} \cos x \sqrt{9-\sin ^{2} x}+\frac{9}{2} \sin ^{-1}\left(\frac{\sin x}{3}\right)+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sqrt{9-4 x^{2}} d x=?$ A. $\frac{x}{2} \sqrt{9-4 x^{2}}+\frac{9}{4} \sin ^{-1} \frac{2 x}{3}+C$ B. $x \sqrt{9-4 x^{2}}+\frac{9}{2} \sin ^{-1} \frac{2 x}{3}+C$ C. $\frac{x}{2} \sqrt{9-4 x^{2}}-\frac{9}{4} \sin ^{-1} \frac{2 x}{3}+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \sqrt{1-9 x^{2}} d x=?$ A. $\frac{x}{2} \sqrt{1-9 x^{2}}+\frac{1}{18} \sin ^{-1} 3 x+C$ B. $\frac{3 x}{2} \sqrt{1-9 x^{2}}+\frac{1}{6} \sin ^{-1} 3 x+C$ C. $\frac{x}{2} \sqrt{1-9 x^{2}}+\frac{1}{6} \sin ^{-1} 3 x+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \sqrt{4-x^{2}} d x=?$ A. $\frac{x}{2} \sqrt{4-x^{2}}+2 \sin ^{-1} \frac{x}{2}+C$ B. $x \sqrt{4-x^{2}}+\sin ^{-1} \frac{x}{2}+C$ C. $\frac{1}{2} x \sqrt{4-x^{2}}-2 \sin ^{-1} \frac{x}{2}+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{x^{2}}{\sqrt{x^{6}+2 x^{3}+3}} d x=?$ A. $\frac{1}{3} \log \left|\left(x^{3}+1\right)+\sqrt{x^{6}+2 x^{3}+3}\right|+C$ B. $\log \left|x^{3}+\sqrt{x^{6}+2 x^{3}+3}\right|+C$ C. $\frac{1}{3} \log \left|\left(x^{3}+1\right)-\sqrt{x^{6}+2 x^{3}+3}\right|+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{\sqrt{2 \mathrm{x}^{2}+4 \mathrm{x}+6}}=?$ A. $\frac{1}{2} \log \left|(x+1)+\sqrt{x^{2}+2 x+3}\right|+C$ B. $\frac{1}{\sqrt{2}} \log \left|(x+1)+\sqrt{x^{2}+2 x+3}\right|+C$ C. $\frac{1}{\sqrt{2}} \log \left|\mathrm{x}+\sqrt{\mathrm{x}^{2}+2 \mathrm{x}+3}\right|+\mathrm{C}$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{\sqrt{3 \mathrm{x}^{2}+6 \mathrm{x}+12}}=?$ A. $\log \left|(x+1)+\sqrt{x^{2}+2 x+4}\right|+C$ B. $\frac{1}{3} \log \left|(x+1)+\sqrt{x^{2}+2 x+4}\right|+C$ C. $\frac{1}{\sqrt{3}} \log \left|(x+1)+\sqrt{x^{2}+2 x+4}\right|+C$ D. none of these Solution:...
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