Integration by Parts
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Integral Calculus

86277 \(\int \sin ^{4} x d x\) is equal to

1 \(\frac{1}{8}\left[3 x+\frac{\sin 4 x}{4}-\frac{4 \sin 2 x}{2}\right]+c\)
2 \(\frac{1}{8}\left[3 x+\frac{\sin 4 x}{4}+\frac{4 \sin 2 x}{2}\right]+c\)
3 \(\frac{1}{4}\left[3 x+\frac{\sin 4 x}{4}-\frac{4 \cos 2 x}{2}\right]+c\)
4 \(\frac{1}{4}\left[3 x+\frac{\sin 4 x}{4}+\frac{4 \cos 4 x}{2}\right]+c\)
CG PET-2006
Integral Calculus

86278 \(\int \log x d x\) is equal to

1 \(\mathrm{x}+\mathrm{x} \log \mathrm{x}+\mathrm{c}\)
2 \(\mathrm{x} \log \mathrm{x}-\mathrm{x}+\mathrm{c}\)
3 \(x^{2} \log x+c\)
4 \(\frac{1}{x} \log x+x c\)
CG PET-2006
Integral Calculus

86348 \(\int \mathrm{e}^{\mathrm{x}}\left(\frac{\mathrm{x}-1}{\mathrm{x}^{2}}\right) \mathrm{dx}=\)

1 \(\frac{-\mathrm{e}^{\mathrm{x}}}{\mathrm{x}^{2}}+\mathrm{C}\)
2 \(\frac{e^{x}}{x}+C\)
3 \(\frac{-e^{x}}{x}+C\)
4 \(\frac{e^{x}}{x^{2}}+C\)
MHT CET-2021
Integral Calculus

86349 \(\int e^{x}\left(\frac{1+\sin x}{1+\cos x}\right) d x=\)

1 \(e^{x} \cos \frac{x}{2}+C\)
2 \(e^{x} \tan \frac{x}{2}+C\)
3 \(e^{x} \sin \frac{x}{2}+C\)
4 None of these
MHT CET-2021
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Integral Calculus

86277 \(\int \sin ^{4} x d x\) is equal to

1 \(\frac{1}{8}\left[3 x+\frac{\sin 4 x}{4}-\frac{4 \sin 2 x}{2}\right]+c\)
2 \(\frac{1}{8}\left[3 x+\frac{\sin 4 x}{4}+\frac{4 \sin 2 x}{2}\right]+c\)
3 \(\frac{1}{4}\left[3 x+\frac{\sin 4 x}{4}-\frac{4 \cos 2 x}{2}\right]+c\)
4 \(\frac{1}{4}\left[3 x+\frac{\sin 4 x}{4}+\frac{4 \cos 4 x}{2}\right]+c\)
CG PET-2006
Integral Calculus

86278 \(\int \log x d x\) is equal to

1 \(\mathrm{x}+\mathrm{x} \log \mathrm{x}+\mathrm{c}\)
2 \(\mathrm{x} \log \mathrm{x}-\mathrm{x}+\mathrm{c}\)
3 \(x^{2} \log x+c\)
4 \(\frac{1}{x} \log x+x c\)
CG PET-2006
Integral Calculus

86348 \(\int \mathrm{e}^{\mathrm{x}}\left(\frac{\mathrm{x}-1}{\mathrm{x}^{2}}\right) \mathrm{dx}=\)

1 \(\frac{-\mathrm{e}^{\mathrm{x}}}{\mathrm{x}^{2}}+\mathrm{C}\)
2 \(\frac{e^{x}}{x}+C\)
3 \(\frac{-e^{x}}{x}+C\)
4 \(\frac{e^{x}}{x^{2}}+C\)
MHT CET-2021
Integral Calculus

86349 \(\int e^{x}\left(\frac{1+\sin x}{1+\cos x}\right) d x=\)

1 \(e^{x} \cos \frac{x}{2}+C\)
2 \(e^{x} \tan \frac{x}{2}+C\)
3 \(e^{x} \sin \frac{x}{2}+C\)
4 None of these
MHT CET-2021
NEET DIGITAL LIBRARY
Integral Calculus

86277 \(\int \sin ^{4} x d x\) is equal to

1 \(\frac{1}{8}\left[3 x+\frac{\sin 4 x}{4}-\frac{4 \sin 2 x}{2}\right]+c\)
2 \(\frac{1}{8}\left[3 x+\frac{\sin 4 x}{4}+\frac{4 \sin 2 x}{2}\right]+c\)
3 \(\frac{1}{4}\left[3 x+\frac{\sin 4 x}{4}-\frac{4 \cos 2 x}{2}\right]+c\)
4 \(\frac{1}{4}\left[3 x+\frac{\sin 4 x}{4}+\frac{4 \cos 4 x}{2}\right]+c\)
CG PET-2006
Integral Calculus

86278 \(\int \log x d x\) is equal to

1 \(\mathrm{x}+\mathrm{x} \log \mathrm{x}+\mathrm{c}\)
2 \(\mathrm{x} \log \mathrm{x}-\mathrm{x}+\mathrm{c}\)
3 \(x^{2} \log x+c\)
4 \(\frac{1}{x} \log x+x c\)
CG PET-2006
Integral Calculus

86348 \(\int \mathrm{e}^{\mathrm{x}}\left(\frac{\mathrm{x}-1}{\mathrm{x}^{2}}\right) \mathrm{dx}=\)

1 \(\frac{-\mathrm{e}^{\mathrm{x}}}{\mathrm{x}^{2}}+\mathrm{C}\)
2 \(\frac{e^{x}}{x}+C\)
3 \(\frac{-e^{x}}{x}+C\)
4 \(\frac{e^{x}}{x^{2}}+C\)
MHT CET-2021
Integral Calculus

86349 \(\int e^{x}\left(\frac{1+\sin x}{1+\cos x}\right) d x=\)

1 \(e^{x} \cos \frac{x}{2}+C\)
2 \(e^{x} \tan \frac{x}{2}+C\)
3 \(e^{x} \sin \frac{x}{2}+C\)
4 None of these
MHT CET-2021
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Integral Calculus

86277 \(\int \sin ^{4} x d x\) is equal to

1 \(\frac{1}{8}\left[3 x+\frac{\sin 4 x}{4}-\frac{4 \sin 2 x}{2}\right]+c\)
2 \(\frac{1}{8}\left[3 x+\frac{\sin 4 x}{4}+\frac{4 \sin 2 x}{2}\right]+c\)
3 \(\frac{1}{4}\left[3 x+\frac{\sin 4 x}{4}-\frac{4 \cos 2 x}{2}\right]+c\)
4 \(\frac{1}{4}\left[3 x+\frac{\sin 4 x}{4}+\frac{4 \cos 4 x}{2}\right]+c\)
CG PET-2006
Integral Calculus

86278 \(\int \log x d x\) is equal to

1 \(\mathrm{x}+\mathrm{x} \log \mathrm{x}+\mathrm{c}\)
2 \(\mathrm{x} \log \mathrm{x}-\mathrm{x}+\mathrm{c}\)
3 \(x^{2} \log x+c\)
4 \(\frac{1}{x} \log x+x c\)
CG PET-2006
Integral Calculus

86348 \(\int \mathrm{e}^{\mathrm{x}}\left(\frac{\mathrm{x}-1}{\mathrm{x}^{2}}\right) \mathrm{dx}=\)

1 \(\frac{-\mathrm{e}^{\mathrm{x}}}{\mathrm{x}^{2}}+\mathrm{C}\)
2 \(\frac{e^{x}}{x}+C\)
3 \(\frac{-e^{x}}{x}+C\)
4 \(\frac{e^{x}}{x^{2}}+C\)
MHT CET-2021
Integral Calculus

86349 \(\int e^{x}\left(\frac{1+\sin x}{1+\cos x}\right) d x=\)

1 \(e^{x} \cos \frac{x}{2}+C\)
2 \(e^{x} \tan \frac{x}{2}+C\)
3 \(e^{x} \sin \frac{x}{2}+C\)
4 None of these
MHT CET-2021
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