Integrations and Integration of Functions
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Integral Calculus

86138 If \(\int \frac{7 x^{8}+8 x^{7}}{\left(1+x+x^{8}\right)^{2}} d x=f(x)+c\), then \(f(x)\) is equal

1 \(\frac{\mathrm{x}^{8}}{1+\mathrm{x}+\mathrm{x}^{8}}\)
2 \(28 \log \left(1+\mathrm{x}+\mathrm{x}^{8}\right)\)
3 \(\frac{1}{1+x+x^{8}}\)
4 \(\frac{-1}{1+x+x^{8}}\)
AP EAMCET-2010
Integral Calculus

86139 If \(f_{n}(x)=\log \log \log \ldots . \log x(\log\) is repeated \(n-\) times), then
\(\int\left(\mathrm{xf}_{1}(\mathrm{x}) \mathrm{f}_{2}(\mathrm{x}) \ldots \ldots \ldots \mathrm{f}_{\mathrm{n}}(\mathrm{x})\right)^{-1} \mathrm{dx}\) is equal to

1 \(f_{n+1}(x)+c\)
2 \(\frac{f_{n+1}(x)}{n+1}+c\)
3 \(\mathrm{nf}_{\mathrm{n}}(\mathrm{x})+\mathrm{c}\)
4 \(\frac{f_{n}(x)}{n}+c\)
AP EAMCET-2010
Integral Calculus

86140 \(\int \frac{d x}{(x+1) \sqrt{4 x+3}}\) is equal to

1 \(\tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
2 \(3 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
3 \(2 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
4 \(4 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
AP EAMCET-2009
Integral Calculus

86141 \(\int\left(\frac{2-\sin 2 x}{1-\cos 2 x}\right) e^{x} d x\) is equal to

1 \(-e^{x} \cot \mathrm{x}+\mathrm{c}\)
2 \(e^{\mathrm{x}} \cot \mathrm{x}+\mathrm{c}\)
3 \(2 e^{x} \cot \mathrm{x}+\mathrm{c}\)
4 \(-2 e^{\mathrm{x}} \cot \mathrm{x}+\mathrm{c}\)
AP EAMCET-2009
Integral Calculus

86142 If \(\int \sqrt{\frac{x}{a^{3}-x^{3}}} d x=g(x)+c\), then \(g(x)\) is equal to:

1 \(\frac{2}{3} \cos ^{-1} \mathrm{x}\)
2 \(\frac{2}{3} \sin ^{-1}\left(\frac{\mathrm{x}^{3}}{\mathrm{a}^{3}}\right)\)
3 \(\frac{2}{3} \sin ^{-1}\left(\sqrt{\frac{\mathrm{x}^{3}}{\mathrm{a}^{3}}}\right)\)
4 \(\frac{2}{3} \cos ^{-1}\left(\frac{\mathrm{x}}{\mathrm{a}}\right)\)
AP EAMCET-2006
NEET DIGITAL LIBRARY
Integral Calculus

86138 If \(\int \frac{7 x^{8}+8 x^{7}}{\left(1+x+x^{8}\right)^{2}} d x=f(x)+c\), then \(f(x)\) is equal

1 \(\frac{\mathrm{x}^{8}}{1+\mathrm{x}+\mathrm{x}^{8}}\)
2 \(28 \log \left(1+\mathrm{x}+\mathrm{x}^{8}\right)\)
3 \(\frac{1}{1+x+x^{8}}\)
4 \(\frac{-1}{1+x+x^{8}}\)
AP EAMCET-2010
Integral Calculus

86139 If \(f_{n}(x)=\log \log \log \ldots . \log x(\log\) is repeated \(n-\) times), then
\(\int\left(\mathrm{xf}_{1}(\mathrm{x}) \mathrm{f}_{2}(\mathrm{x}) \ldots \ldots \ldots \mathrm{f}_{\mathrm{n}}(\mathrm{x})\right)^{-1} \mathrm{dx}\) is equal to

1 \(f_{n+1}(x)+c\)
2 \(\frac{f_{n+1}(x)}{n+1}+c\)
3 \(\mathrm{nf}_{\mathrm{n}}(\mathrm{x})+\mathrm{c}\)
4 \(\frac{f_{n}(x)}{n}+c\)
AP EAMCET-2010
Integral Calculus

86140 \(\int \frac{d x}{(x+1) \sqrt{4 x+3}}\) is equal to

1 \(\tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
2 \(3 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
3 \(2 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
4 \(4 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
AP EAMCET-2009
Integral Calculus

86141 \(\int\left(\frac{2-\sin 2 x}{1-\cos 2 x}\right) e^{x} d x\) is equal to

1 \(-e^{x} \cot \mathrm{x}+\mathrm{c}\)
2 \(e^{\mathrm{x}} \cot \mathrm{x}+\mathrm{c}\)
3 \(2 e^{x} \cot \mathrm{x}+\mathrm{c}\)
4 \(-2 e^{\mathrm{x}} \cot \mathrm{x}+\mathrm{c}\)
AP EAMCET-2009
Integral Calculus

86142 If \(\int \sqrt{\frac{x}{a^{3}-x^{3}}} d x=g(x)+c\), then \(g(x)\) is equal to:

1 \(\frac{2}{3} \cos ^{-1} \mathrm{x}\)
2 \(\frac{2}{3} \sin ^{-1}\left(\frac{\mathrm{x}^{3}}{\mathrm{a}^{3}}\right)\)
3 \(\frac{2}{3} \sin ^{-1}\left(\sqrt{\frac{\mathrm{x}^{3}}{\mathrm{a}^{3}}}\right)\)
4 \(\frac{2}{3} \cos ^{-1}\left(\frac{\mathrm{x}}{\mathrm{a}}\right)\)
AP EAMCET-2006
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Integral Calculus

86138 If \(\int \frac{7 x^{8}+8 x^{7}}{\left(1+x+x^{8}\right)^{2}} d x=f(x)+c\), then \(f(x)\) is equal

1 \(\frac{\mathrm{x}^{8}}{1+\mathrm{x}+\mathrm{x}^{8}}\)
2 \(28 \log \left(1+\mathrm{x}+\mathrm{x}^{8}\right)\)
3 \(\frac{1}{1+x+x^{8}}\)
4 \(\frac{-1}{1+x+x^{8}}\)
AP EAMCET-2010
Integral Calculus

86139 If \(f_{n}(x)=\log \log \log \ldots . \log x(\log\) is repeated \(n-\) times), then
\(\int\left(\mathrm{xf}_{1}(\mathrm{x}) \mathrm{f}_{2}(\mathrm{x}) \ldots \ldots \ldots \mathrm{f}_{\mathrm{n}}(\mathrm{x})\right)^{-1} \mathrm{dx}\) is equal to

1 \(f_{n+1}(x)+c\)
2 \(\frac{f_{n+1}(x)}{n+1}+c\)
3 \(\mathrm{nf}_{\mathrm{n}}(\mathrm{x})+\mathrm{c}\)
4 \(\frac{f_{n}(x)}{n}+c\)
AP EAMCET-2010
Integral Calculus

86140 \(\int \frac{d x}{(x+1) \sqrt{4 x+3}}\) is equal to

1 \(\tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
2 \(3 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
3 \(2 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
4 \(4 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
AP EAMCET-2009
Integral Calculus

86141 \(\int\left(\frac{2-\sin 2 x}{1-\cos 2 x}\right) e^{x} d x\) is equal to

1 \(-e^{x} \cot \mathrm{x}+\mathrm{c}\)
2 \(e^{\mathrm{x}} \cot \mathrm{x}+\mathrm{c}\)
3 \(2 e^{x} \cot \mathrm{x}+\mathrm{c}\)
4 \(-2 e^{\mathrm{x}} \cot \mathrm{x}+\mathrm{c}\)
AP EAMCET-2009
Integral Calculus

86142 If \(\int \sqrt{\frac{x}{a^{3}-x^{3}}} d x=g(x)+c\), then \(g(x)\) is equal to:

1 \(\frac{2}{3} \cos ^{-1} \mathrm{x}\)
2 \(\frac{2}{3} \sin ^{-1}\left(\frac{\mathrm{x}^{3}}{\mathrm{a}^{3}}\right)\)
3 \(\frac{2}{3} \sin ^{-1}\left(\sqrt{\frac{\mathrm{x}^{3}}{\mathrm{a}^{3}}}\right)\)
4 \(\frac{2}{3} \cos ^{-1}\left(\frac{\mathrm{x}}{\mathrm{a}}\right)\)
AP EAMCET-2006
For More Updates join with Us
Integral Calculus

86138 If \(\int \frac{7 x^{8}+8 x^{7}}{\left(1+x+x^{8}\right)^{2}} d x=f(x)+c\), then \(f(x)\) is equal

1 \(\frac{\mathrm{x}^{8}}{1+\mathrm{x}+\mathrm{x}^{8}}\)
2 \(28 \log \left(1+\mathrm{x}+\mathrm{x}^{8}\right)\)
3 \(\frac{1}{1+x+x^{8}}\)
4 \(\frac{-1}{1+x+x^{8}}\)
AP EAMCET-2010
Integral Calculus

86139 If \(f_{n}(x)=\log \log \log \ldots . \log x(\log\) is repeated \(n-\) times), then
\(\int\left(\mathrm{xf}_{1}(\mathrm{x}) \mathrm{f}_{2}(\mathrm{x}) \ldots \ldots \ldots \mathrm{f}_{\mathrm{n}}(\mathrm{x})\right)^{-1} \mathrm{dx}\) is equal to

1 \(f_{n+1}(x)+c\)
2 \(\frac{f_{n+1}(x)}{n+1}+c\)
3 \(\mathrm{nf}_{\mathrm{n}}(\mathrm{x})+\mathrm{c}\)
4 \(\frac{f_{n}(x)}{n}+c\)
AP EAMCET-2010
Integral Calculus

86140 \(\int \frac{d x}{(x+1) \sqrt{4 x+3}}\) is equal to

1 \(\tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
2 \(3 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
3 \(2 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
4 \(4 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
AP EAMCET-2009
Integral Calculus

86141 \(\int\left(\frac{2-\sin 2 x}{1-\cos 2 x}\right) e^{x} d x\) is equal to

1 \(-e^{x} \cot \mathrm{x}+\mathrm{c}\)
2 \(e^{\mathrm{x}} \cot \mathrm{x}+\mathrm{c}\)
3 \(2 e^{x} \cot \mathrm{x}+\mathrm{c}\)
4 \(-2 e^{\mathrm{x}} \cot \mathrm{x}+\mathrm{c}\)
AP EAMCET-2009
Integral Calculus

86142 If \(\int \sqrt{\frac{x}{a^{3}-x^{3}}} d x=g(x)+c\), then \(g(x)\) is equal to:

1 \(\frac{2}{3} \cos ^{-1} \mathrm{x}\)
2 \(\frac{2}{3} \sin ^{-1}\left(\frac{\mathrm{x}^{3}}{\mathrm{a}^{3}}\right)\)
3 \(\frac{2}{3} \sin ^{-1}\left(\sqrt{\frac{\mathrm{x}^{3}}{\mathrm{a}^{3}}}\right)\)
4 \(\frac{2}{3} \cos ^{-1}\left(\frac{\mathrm{x}}{\mathrm{a}}\right)\)
AP EAMCET-2006
NEET DIGITAL LIBRARY
Integral Calculus

86138 If \(\int \frac{7 x^{8}+8 x^{7}}{\left(1+x+x^{8}\right)^{2}} d x=f(x)+c\), then \(f(x)\) is equal

1 \(\frac{\mathrm{x}^{8}}{1+\mathrm{x}+\mathrm{x}^{8}}\)
2 \(28 \log \left(1+\mathrm{x}+\mathrm{x}^{8}\right)\)
3 \(\frac{1}{1+x+x^{8}}\)
4 \(\frac{-1}{1+x+x^{8}}\)
AP EAMCET-2010
Integral Calculus

86139 If \(f_{n}(x)=\log \log \log \ldots . \log x(\log\) is repeated \(n-\) times), then
\(\int\left(\mathrm{xf}_{1}(\mathrm{x}) \mathrm{f}_{2}(\mathrm{x}) \ldots \ldots \ldots \mathrm{f}_{\mathrm{n}}(\mathrm{x})\right)^{-1} \mathrm{dx}\) is equal to

1 \(f_{n+1}(x)+c\)
2 \(\frac{f_{n+1}(x)}{n+1}+c\)
3 \(\mathrm{nf}_{\mathrm{n}}(\mathrm{x})+\mathrm{c}\)
4 \(\frac{f_{n}(x)}{n}+c\)
AP EAMCET-2010
Integral Calculus

86140 \(\int \frac{d x}{(x+1) \sqrt{4 x+3}}\) is equal to

1 \(\tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
2 \(3 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
3 \(2 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
4 \(4 \tan ^{-1} \sqrt{4 \mathrm{x}+3}+\mathrm{c}\)
AP EAMCET-2009
Integral Calculus

86141 \(\int\left(\frac{2-\sin 2 x}{1-\cos 2 x}\right) e^{x} d x\) is equal to

1 \(-e^{x} \cot \mathrm{x}+\mathrm{c}\)
2 \(e^{\mathrm{x}} \cot \mathrm{x}+\mathrm{c}\)
3 \(2 e^{x} \cot \mathrm{x}+\mathrm{c}\)
4 \(-2 e^{\mathrm{x}} \cot \mathrm{x}+\mathrm{c}\)
AP EAMCET-2009
Integral Calculus

86142 If \(\int \sqrt{\frac{x}{a^{3}-x^{3}}} d x=g(x)+c\), then \(g(x)\) is equal to:

1 \(\frac{2}{3} \cos ^{-1} \mathrm{x}\)
2 \(\frac{2}{3} \sin ^{-1}\left(\frac{\mathrm{x}^{3}}{\mathrm{a}^{3}}\right)\)
3 \(\frac{2}{3} \sin ^{-1}\left(\sqrt{\frac{\mathrm{x}^{3}}{\mathrm{a}^{3}}}\right)\)
4 \(\frac{2}{3} \cos ^{-1}\left(\frac{\mathrm{x}}{\mathrm{a}}\right)\)
AP EAMCET-2006