Integration by Parts
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Integral Calculus

86263 \(\int\left(1+x-x^{-1}\right) e^{x+x^{-1}} d x\) is equal to

1 \((\mathrm{x}+1) \mathrm{e}^{\mathrm{x}+\mathrm{x}^{-1}}+\mathrm{C}\)
2 \((\mathrm{x}-1) \mathrm{e}^{\mathrm{x}+\mathrm{x}^{-1}}+\mathrm{C}\)
3 \(\mathrm{xe}^{\mathrm{x+x}}+\mathrm{C}\)
4 \(\mathrm{xe}^{\mathrm{x}+\mathrm{x}^{-1}} \mathrm{x}+\mathrm{C}\)
VITEEE-2013
Integral Calculus

86264 Integral of \(\frac{1}{2+\cos x}\) is

1 \(\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{1}{2} \tan x\right)+C\)
2 \(\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{1}{\sqrt{3}} \tan \frac{x}{2}\right)+C\)
3 \(-\sin x \log (2+\cos x)+C\)
4 \(\sin x \log (2+\cos x)+C\)
UPSEE-2016
Integral Calculus

86265 \(\int \frac{d x}{\sin x-\cos x+\sqrt{2}}\) is equal to

1 \(-\frac{1}{\sqrt{2}} \tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
2 \(\frac{1}{\sqrt{2}} \tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
3 \(\frac{1}{\sqrt{2}} \cot \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
4 \(-\frac{1}{\sqrt{2}} \cot \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
UPSEE-2012
Integral Calculus

86266 \(\int e^{x} \frac{x^{2}+1}{(x+1)^{2}} d x\) is equal to

1 \(\frac{-e^{x}}{x+1}+c\)
2 \(\frac{e^{x}}{x+1}+c\)
3 \(e^{x} \frac{x-1}{x+1}+c\)
4 \(\frac{x e^{x}}{x+1}+c\)
UPSEE-2009
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Integral Calculus

86263 \(\int\left(1+x-x^{-1}\right) e^{x+x^{-1}} d x\) is equal to

1 \((\mathrm{x}+1) \mathrm{e}^{\mathrm{x}+\mathrm{x}^{-1}}+\mathrm{C}\)
2 \((\mathrm{x}-1) \mathrm{e}^{\mathrm{x}+\mathrm{x}^{-1}}+\mathrm{C}\)
3 \(\mathrm{xe}^{\mathrm{x+x}}+\mathrm{C}\)
4 \(\mathrm{xe}^{\mathrm{x}+\mathrm{x}^{-1}} \mathrm{x}+\mathrm{C}\)
VITEEE-2013
Integral Calculus

86264 Integral of \(\frac{1}{2+\cos x}\) is

1 \(\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{1}{2} \tan x\right)+C\)
2 \(\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{1}{\sqrt{3}} \tan \frac{x}{2}\right)+C\)
3 \(-\sin x \log (2+\cos x)+C\)
4 \(\sin x \log (2+\cos x)+C\)
UPSEE-2016
Integral Calculus

86265 \(\int \frac{d x}{\sin x-\cos x+\sqrt{2}}\) is equal to

1 \(-\frac{1}{\sqrt{2}} \tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
2 \(\frac{1}{\sqrt{2}} \tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
3 \(\frac{1}{\sqrt{2}} \cot \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
4 \(-\frac{1}{\sqrt{2}} \cot \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
UPSEE-2012
Integral Calculus

86266 \(\int e^{x} \frac{x^{2}+1}{(x+1)^{2}} d x\) is equal to

1 \(\frac{-e^{x}}{x+1}+c\)
2 \(\frac{e^{x}}{x+1}+c\)
3 \(e^{x} \frac{x-1}{x+1}+c\)
4 \(\frac{x e^{x}}{x+1}+c\)
UPSEE-2009
NEET DIGITAL LIBRARY
Integral Calculus

86263 \(\int\left(1+x-x^{-1}\right) e^{x+x^{-1}} d x\) is equal to

1 \((\mathrm{x}+1) \mathrm{e}^{\mathrm{x}+\mathrm{x}^{-1}}+\mathrm{C}\)
2 \((\mathrm{x}-1) \mathrm{e}^{\mathrm{x}+\mathrm{x}^{-1}}+\mathrm{C}\)
3 \(\mathrm{xe}^{\mathrm{x+x}}+\mathrm{C}\)
4 \(\mathrm{xe}^{\mathrm{x}+\mathrm{x}^{-1}} \mathrm{x}+\mathrm{C}\)
VITEEE-2013
Integral Calculus

86264 Integral of \(\frac{1}{2+\cos x}\) is

1 \(\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{1}{2} \tan x\right)+C\)
2 \(\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{1}{\sqrt{3}} \tan \frac{x}{2}\right)+C\)
3 \(-\sin x \log (2+\cos x)+C\)
4 \(\sin x \log (2+\cos x)+C\)
UPSEE-2016
Integral Calculus

86265 \(\int \frac{d x}{\sin x-\cos x+\sqrt{2}}\) is equal to

1 \(-\frac{1}{\sqrt{2}} \tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
2 \(\frac{1}{\sqrt{2}} \tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
3 \(\frac{1}{\sqrt{2}} \cot \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
4 \(-\frac{1}{\sqrt{2}} \cot \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
UPSEE-2012
Integral Calculus

86266 \(\int e^{x} \frac{x^{2}+1}{(x+1)^{2}} d x\) is equal to

1 \(\frac{-e^{x}}{x+1}+c\)
2 \(\frac{e^{x}}{x+1}+c\)
3 \(e^{x} \frac{x-1}{x+1}+c\)
4 \(\frac{x e^{x}}{x+1}+c\)
UPSEE-2009
Join With Us for More Updates
Integral Calculus

86263 \(\int\left(1+x-x^{-1}\right) e^{x+x^{-1}} d x\) is equal to

1 \((\mathrm{x}+1) \mathrm{e}^{\mathrm{x}+\mathrm{x}^{-1}}+\mathrm{C}\)
2 \((\mathrm{x}-1) \mathrm{e}^{\mathrm{x}+\mathrm{x}^{-1}}+\mathrm{C}\)
3 \(\mathrm{xe}^{\mathrm{x+x}}+\mathrm{C}\)
4 \(\mathrm{xe}^{\mathrm{x}+\mathrm{x}^{-1}} \mathrm{x}+\mathrm{C}\)
VITEEE-2013
Integral Calculus

86264 Integral of \(\frac{1}{2+\cos x}\) is

1 \(\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{1}{2} \tan x\right)+C\)
2 \(\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{1}{\sqrt{3}} \tan \frac{x}{2}\right)+C\)
3 \(-\sin x \log (2+\cos x)+C\)
4 \(\sin x \log (2+\cos x)+C\)
UPSEE-2016
Integral Calculus

86265 \(\int \frac{d x}{\sin x-\cos x+\sqrt{2}}\) is equal to

1 \(-\frac{1}{\sqrt{2}} \tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
2 \(\frac{1}{\sqrt{2}} \tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
3 \(\frac{1}{\sqrt{2}} \cot \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
4 \(-\frac{1}{\sqrt{2}} \cot \left(\frac{\mathrm{x}}{2}+\frac{\pi}{8}\right)+\mathrm{C}\)
UPSEE-2012
Integral Calculus

86266 \(\int e^{x} \frac{x^{2}+1}{(x+1)^{2}} d x\) is equal to

1 \(\frac{-e^{x}}{x+1}+c\)
2 \(\frac{e^{x}}{x+1}+c\)
3 \(e^{x} \frac{x-1}{x+1}+c\)
4 \(\frac{x e^{x}}{x+1}+c\)
UPSEE-2009
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