Integration by Parts
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Integral Calculus

86270 \(\int \mathrm{e}^{\mathrm{xlog} a} \mathrm{e}^{\mathrm{x}} \mathrm{dx}\) is equal to

1 \((a)^{x}+C\)
2 \(\frac{(\text { ae })^{\mathrm{x}}}{\log (\mathrm{ae})}+\mathrm{C}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}}{1+\log \mathrm{a}}+\mathrm{C}\)
4 none of these
AMU-2010
Integral Calculus

86272 \(\int \mathrm{e}^{x}(1+\tan x) \sec x d x=a\)

1 \(e^{x} \sec x\)
2 \(e^{x} \cos \mathrm{x}\)
3 \(e^{x} \cot x\)
4 \(e^{x} \tan x\)
CG PET-2018
Integral Calculus

86276 \(\int e^{x} \sin \left(e^{x}\right) d x\) is equal to

1 \(-\cos \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
2 \(\cos \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
3 \(-\operatorname{cosec} \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
4 None of these
CG PET-2006
Integral Calculus

86218 The value of \(\int x^{3} \log x d x\) is :

1 \(\frac{1}{16}\left(4 x^{4} \log x-x^{4}+C\right)\)
2 \(\frac{1}{8}\left(x^{4} \log x-4 x^{4}+C\right)\)
3 \(\frac{1}{16}\left(4 x^{4} \log x+x^{4}+C\right)\)
4 \(\frac{x^{4} \log x}{4}+C\)
Karnataka CET-2002
Integral Calculus

86220 \(\int \frac{(x+3) e^{x}}{(x+4)^{2}} d x\) is equal to

1 \(\frac{e^{x}}{(x+4)}+C\)
2 \(\frac{\mathrm{e}^{\mathrm{x}}}{(\mathrm{x}+4)^{2}}+\mathrm{C}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}}{(\mathrm{x}+3)}+\mathrm{C}\)
4 \(\frac{1}{(x+4)^{2}}+C\)
Karnataka CET-2017
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Integral Calculus

86270 \(\int \mathrm{e}^{\mathrm{xlog} a} \mathrm{e}^{\mathrm{x}} \mathrm{dx}\) is equal to

1 \((a)^{x}+C\)
2 \(\frac{(\text { ae })^{\mathrm{x}}}{\log (\mathrm{ae})}+\mathrm{C}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}}{1+\log \mathrm{a}}+\mathrm{C}\)
4 none of these
AMU-2010
Integral Calculus

86272 \(\int \mathrm{e}^{x}(1+\tan x) \sec x d x=a\)

1 \(e^{x} \sec x\)
2 \(e^{x} \cos \mathrm{x}\)
3 \(e^{x} \cot x\)
4 \(e^{x} \tan x\)
CG PET-2018
Integral Calculus

86276 \(\int e^{x} \sin \left(e^{x}\right) d x\) is equal to

1 \(-\cos \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
2 \(\cos \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
3 \(-\operatorname{cosec} \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
4 None of these
CG PET-2006
Integral Calculus

86218 The value of \(\int x^{3} \log x d x\) is :

1 \(\frac{1}{16}\left(4 x^{4} \log x-x^{4}+C\right)\)
2 \(\frac{1}{8}\left(x^{4} \log x-4 x^{4}+C\right)\)
3 \(\frac{1}{16}\left(4 x^{4} \log x+x^{4}+C\right)\)
4 \(\frac{x^{4} \log x}{4}+C\)
Karnataka CET-2002
Integral Calculus

86220 \(\int \frac{(x+3) e^{x}}{(x+4)^{2}} d x\) is equal to

1 \(\frac{e^{x}}{(x+4)}+C\)
2 \(\frac{\mathrm{e}^{\mathrm{x}}}{(\mathrm{x}+4)^{2}}+\mathrm{C}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}}{(\mathrm{x}+3)}+\mathrm{C}\)
4 \(\frac{1}{(x+4)^{2}}+C\)
Karnataka CET-2017
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Integral Calculus

86270 \(\int \mathrm{e}^{\mathrm{xlog} a} \mathrm{e}^{\mathrm{x}} \mathrm{dx}\) is equal to

1 \((a)^{x}+C\)
2 \(\frac{(\text { ae })^{\mathrm{x}}}{\log (\mathrm{ae})}+\mathrm{C}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}}{1+\log \mathrm{a}}+\mathrm{C}\)
4 none of these
AMU-2010
Integral Calculus

86272 \(\int \mathrm{e}^{x}(1+\tan x) \sec x d x=a\)

1 \(e^{x} \sec x\)
2 \(e^{x} \cos \mathrm{x}\)
3 \(e^{x} \cot x\)
4 \(e^{x} \tan x\)
CG PET-2018
Integral Calculus

86276 \(\int e^{x} \sin \left(e^{x}\right) d x\) is equal to

1 \(-\cos \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
2 \(\cos \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
3 \(-\operatorname{cosec} \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
4 None of these
CG PET-2006
Integral Calculus

86218 The value of \(\int x^{3} \log x d x\) is :

1 \(\frac{1}{16}\left(4 x^{4} \log x-x^{4}+C\right)\)
2 \(\frac{1}{8}\left(x^{4} \log x-4 x^{4}+C\right)\)
3 \(\frac{1}{16}\left(4 x^{4} \log x+x^{4}+C\right)\)
4 \(\frac{x^{4} \log x}{4}+C\)
Karnataka CET-2002
Integral Calculus

86220 \(\int \frac{(x+3) e^{x}}{(x+4)^{2}} d x\) is equal to

1 \(\frac{e^{x}}{(x+4)}+C\)
2 \(\frac{\mathrm{e}^{\mathrm{x}}}{(\mathrm{x}+4)^{2}}+\mathrm{C}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}}{(\mathrm{x}+3)}+\mathrm{C}\)
4 \(\frac{1}{(x+4)^{2}}+C\)
Karnataka CET-2017
NEET DIGITAL LIBRARY
Integral Calculus

86270 \(\int \mathrm{e}^{\mathrm{xlog} a} \mathrm{e}^{\mathrm{x}} \mathrm{dx}\) is equal to

1 \((a)^{x}+C\)
2 \(\frac{(\text { ae })^{\mathrm{x}}}{\log (\mathrm{ae})}+\mathrm{C}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}}{1+\log \mathrm{a}}+\mathrm{C}\)
4 none of these
AMU-2010
Integral Calculus

86272 \(\int \mathrm{e}^{x}(1+\tan x) \sec x d x=a\)

1 \(e^{x} \sec x\)
2 \(e^{x} \cos \mathrm{x}\)
3 \(e^{x} \cot x\)
4 \(e^{x} \tan x\)
CG PET-2018
Integral Calculus

86276 \(\int e^{x} \sin \left(e^{x}\right) d x\) is equal to

1 \(-\cos \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
2 \(\cos \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
3 \(-\operatorname{cosec} \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
4 None of these
CG PET-2006
Integral Calculus

86218 The value of \(\int x^{3} \log x d x\) is :

1 \(\frac{1}{16}\left(4 x^{4} \log x-x^{4}+C\right)\)
2 \(\frac{1}{8}\left(x^{4} \log x-4 x^{4}+C\right)\)
3 \(\frac{1}{16}\left(4 x^{4} \log x+x^{4}+C\right)\)
4 \(\frac{x^{4} \log x}{4}+C\)
Karnataka CET-2002
Integral Calculus

86220 \(\int \frac{(x+3) e^{x}}{(x+4)^{2}} d x\) is equal to

1 \(\frac{e^{x}}{(x+4)}+C\)
2 \(\frac{\mathrm{e}^{\mathrm{x}}}{(\mathrm{x}+4)^{2}}+\mathrm{C}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}}{(\mathrm{x}+3)}+\mathrm{C}\)
4 \(\frac{1}{(x+4)^{2}}+C\)
Karnataka CET-2017
Join With Us for More Updates
Integral Calculus

86270 \(\int \mathrm{e}^{\mathrm{xlog} a} \mathrm{e}^{\mathrm{x}} \mathrm{dx}\) is equal to

1 \((a)^{x}+C\)
2 \(\frac{(\text { ae })^{\mathrm{x}}}{\log (\mathrm{ae})}+\mathrm{C}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}}{1+\log \mathrm{a}}+\mathrm{C}\)
4 none of these
AMU-2010
Integral Calculus

86272 \(\int \mathrm{e}^{x}(1+\tan x) \sec x d x=a\)

1 \(e^{x} \sec x\)
2 \(e^{x} \cos \mathrm{x}\)
3 \(e^{x} \cot x\)
4 \(e^{x} \tan x\)
CG PET-2018
Integral Calculus

86276 \(\int e^{x} \sin \left(e^{x}\right) d x\) is equal to

1 \(-\cos \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
2 \(\cos \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
3 \(-\operatorname{cosec} \mathrm{e}^{\mathrm{x}}+\mathrm{c}\)
4 None of these
CG PET-2006
Integral Calculus

86218 The value of \(\int x^{3} \log x d x\) is :

1 \(\frac{1}{16}\left(4 x^{4} \log x-x^{4}+C\right)\)
2 \(\frac{1}{8}\left(x^{4} \log x-4 x^{4}+C\right)\)
3 \(\frac{1}{16}\left(4 x^{4} \log x+x^{4}+C\right)\)
4 \(\frac{x^{4} \log x}{4}+C\)
Karnataka CET-2002
Integral Calculus

86220 \(\int \frac{(x+3) e^{x}}{(x+4)^{2}} d x\) is equal to

1 \(\frac{e^{x}}{(x+4)}+C\)
2 \(\frac{\mathrm{e}^{\mathrm{x}}}{(\mathrm{x}+4)^{2}}+\mathrm{C}\)
3 \(\frac{\mathrm{e}^{\mathrm{x}}}{(\mathrm{x}+3)}+\mathrm{C}\)
4 \(\frac{1}{(x+4)^{2}}+C\)
Karnataka CET-2017