Integration by Parts
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Integral Calculus

86346 The value of \(\int \frac{2 x^{12}+5 x^{9}}{\left(x^{5}+x^{3}+1\right)^{3}} d x\) is equal to (where \(\mathbf{C}\) is arbitrary constant)

1 \(\frac{x^{5}}{2\left(x^{5}+x^{3}+1\right)^{2}}+C\)
2 \(\frac{x^{10}}{2\left(x^{5}+x^{3}+1\right)^{2}}+C\)
3 \(\frac{-x^{5}}{\left(x^{5}+x^{3}+1\right)^{2}}+C\)
4 \(\frac{-\mathrm{x}^{10}}{2\left(\mathrm{x}^{5}+\mathrm{x}^{3}+1\right)^{2}}+\mathrm{C}\)
MHT CET-2022
Integral Calculus

86347 \(\int \mathrm{e}^{\tan x}\left(\sec ^{2} x+\sec ^{3} x \sin x\right) d x=\)

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

86273 \(\int_{0}^{\pi / 2} \log \sin x d x\) is equal to

1 \(-\frac{\pi}{2} \log 2\)
2 \(\pi \log \frac{1}{2}\)
3 \(-\pi \log \frac{1}{2}\)
4 \(\log 2\)
CG PET-2007
Integral Calculus

86274 \(\int \frac{\sin ^{2} x-\cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x\) is equal to

1 \(\tan x+\cot x+c\)
2 \(\operatorname{cosec} x+\sec x+c\)
3 \(\tan x+\sec x+c\)
4 \(\tan x+\operatorname{cosec} x+c\)
AMU-2002
Integral Calculus

86275 \(\int\left(\frac{x-1}{x^{2}}\right) e^{x} d x\) is equal to

1 \(\mathrm{e}^{\mathrm{x}}+\frac{1}{\mathrm{x}}+\mathrm{c}\)
2 \(\frac{e^{x}}{x}+c\)
3 \(\frac{e^{x}}{x^{2}}+c\)
4 \(\mathrm{e}^{\mathrm{x}}\left(\log \mathrm{x}+\frac{1}{\mathrm{x}}\right)+\mathrm{c}\)
AMU-2002
NEET DIGITAL LIBRARY
Integral Calculus

86346 The value of \(\int \frac{2 x^{12}+5 x^{9}}{\left(x^{5}+x^{3}+1\right)^{3}} d x\) is equal to (where \(\mathbf{C}\) is arbitrary constant)

1 \(\frac{x^{5}}{2\left(x^{5}+x^{3}+1\right)^{2}}+C\)
2 \(\frac{x^{10}}{2\left(x^{5}+x^{3}+1\right)^{2}}+C\)
3 \(\frac{-x^{5}}{\left(x^{5}+x^{3}+1\right)^{2}}+C\)
4 \(\frac{-\mathrm{x}^{10}}{2\left(\mathrm{x}^{5}+\mathrm{x}^{3}+1\right)^{2}}+\mathrm{C}\)
MHT CET-2022
Integral Calculus

86347 \(\int \mathrm{e}^{\tan x}\left(\sec ^{2} x+\sec ^{3} x \sin x\right) d x=\)

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

86273 \(\int_{0}^{\pi / 2} \log \sin x d x\) is equal to

1 \(-\frac{\pi}{2} \log 2\)
2 \(\pi \log \frac{1}{2}\)
3 \(-\pi \log \frac{1}{2}\)
4 \(\log 2\)
CG PET-2007
Integral Calculus

86274 \(\int \frac{\sin ^{2} x-\cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x\) is equal to

1 \(\tan x+\cot x+c\)
2 \(\operatorname{cosec} x+\sec x+c\)
3 \(\tan x+\sec x+c\)
4 \(\tan x+\operatorname{cosec} x+c\)
AMU-2002
Integral Calculus

86275 \(\int\left(\frac{x-1}{x^{2}}\right) e^{x} d x\) is equal to

1 \(\mathrm{e}^{\mathrm{x}}+\frac{1}{\mathrm{x}}+\mathrm{c}\)
2 \(\frac{e^{x}}{x}+c\)
3 \(\frac{e^{x}}{x^{2}}+c\)
4 \(\mathrm{e}^{\mathrm{x}}\left(\log \mathrm{x}+\frac{1}{\mathrm{x}}\right)+\mathrm{c}\)
AMU-2002
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Integral Calculus

86346 The value of \(\int \frac{2 x^{12}+5 x^{9}}{\left(x^{5}+x^{3}+1\right)^{3}} d x\) is equal to (where \(\mathbf{C}\) is arbitrary constant)

1 \(\frac{x^{5}}{2\left(x^{5}+x^{3}+1\right)^{2}}+C\)
2 \(\frac{x^{10}}{2\left(x^{5}+x^{3}+1\right)^{2}}+C\)
3 \(\frac{-x^{5}}{\left(x^{5}+x^{3}+1\right)^{2}}+C\)
4 \(\frac{-\mathrm{x}^{10}}{2\left(\mathrm{x}^{5}+\mathrm{x}^{3}+1\right)^{2}}+\mathrm{C}\)
MHT CET-2022
Integral Calculus

86347 \(\int \mathrm{e}^{\tan x}\left(\sec ^{2} x+\sec ^{3} x \sin x\right) d x=\)

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

86273 \(\int_{0}^{\pi / 2} \log \sin x d x\) is equal to

1 \(-\frac{\pi}{2} \log 2\)
2 \(\pi \log \frac{1}{2}\)
3 \(-\pi \log \frac{1}{2}\)
4 \(\log 2\)
CG PET-2007
Integral Calculus

86274 \(\int \frac{\sin ^{2} x-\cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x\) is equal to

1 \(\tan x+\cot x+c\)
2 \(\operatorname{cosec} x+\sec x+c\)
3 \(\tan x+\sec x+c\)
4 \(\tan x+\operatorname{cosec} x+c\)
AMU-2002
Integral Calculus

86275 \(\int\left(\frac{x-1}{x^{2}}\right) e^{x} d x\) is equal to

1 \(\mathrm{e}^{\mathrm{x}}+\frac{1}{\mathrm{x}}+\mathrm{c}\)
2 \(\frac{e^{x}}{x}+c\)
3 \(\frac{e^{x}}{x^{2}}+c\)
4 \(\mathrm{e}^{\mathrm{x}}\left(\log \mathrm{x}+\frac{1}{\mathrm{x}}\right)+\mathrm{c}\)
AMU-2002
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Integral Calculus

86346 The value of \(\int \frac{2 x^{12}+5 x^{9}}{\left(x^{5}+x^{3}+1\right)^{3}} d x\) is equal to (where \(\mathbf{C}\) is arbitrary constant)

1 \(\frac{x^{5}}{2\left(x^{5}+x^{3}+1\right)^{2}}+C\)
2 \(\frac{x^{10}}{2\left(x^{5}+x^{3}+1\right)^{2}}+C\)
3 \(\frac{-x^{5}}{\left(x^{5}+x^{3}+1\right)^{2}}+C\)
4 \(\frac{-\mathrm{x}^{10}}{2\left(\mathrm{x}^{5}+\mathrm{x}^{3}+1\right)^{2}}+\mathrm{C}\)
MHT CET-2022
Integral Calculus

86347 \(\int \mathrm{e}^{\tan x}\left(\sec ^{2} x+\sec ^{3} x \sin x\right) d x=\)

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

86273 \(\int_{0}^{\pi / 2} \log \sin x d x\) is equal to

1 \(-\frac{\pi}{2} \log 2\)
2 \(\pi \log \frac{1}{2}\)
3 \(-\pi \log \frac{1}{2}\)
4 \(\log 2\)
CG PET-2007
Integral Calculus

86274 \(\int \frac{\sin ^{2} x-\cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x\) is equal to

1 \(\tan x+\cot x+c\)
2 \(\operatorname{cosec} x+\sec x+c\)
3 \(\tan x+\sec x+c\)
4 \(\tan x+\operatorname{cosec} x+c\)
AMU-2002
Integral Calculus

86275 \(\int\left(\frac{x-1}{x^{2}}\right) e^{x} d x\) is equal to

1 \(\mathrm{e}^{\mathrm{x}}+\frac{1}{\mathrm{x}}+\mathrm{c}\)
2 \(\frac{e^{x}}{x}+c\)
3 \(\frac{e^{x}}{x^{2}}+c\)
4 \(\mathrm{e}^{\mathrm{x}}\left(\log \mathrm{x}+\frac{1}{\mathrm{x}}\right)+\mathrm{c}\)
AMU-2002
NEET DIGITAL LIBRARY
Integral Calculus

86346 The value of \(\int \frac{2 x^{12}+5 x^{9}}{\left(x^{5}+x^{3}+1\right)^{3}} d x\) is equal to (where \(\mathbf{C}\) is arbitrary constant)

1 \(\frac{x^{5}}{2\left(x^{5}+x^{3}+1\right)^{2}}+C\)
2 \(\frac{x^{10}}{2\left(x^{5}+x^{3}+1\right)^{2}}+C\)
3 \(\frac{-x^{5}}{\left(x^{5}+x^{3}+1\right)^{2}}+C\)
4 \(\frac{-\mathrm{x}^{10}}{2\left(\mathrm{x}^{5}+\mathrm{x}^{3}+1\right)^{2}}+\mathrm{C}\)
MHT CET-2022
Integral Calculus

86347 \(\int \mathrm{e}^{\tan x}\left(\sec ^{2} x+\sec ^{3} x \sin x\right) d x=\)

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

86273 \(\int_{0}^{\pi / 2} \log \sin x d x\) is equal to

1 \(-\frac{\pi}{2} \log 2\)
2 \(\pi \log \frac{1}{2}\)
3 \(-\pi \log \frac{1}{2}\)
4 \(\log 2\)
CG PET-2007
Integral Calculus

86274 \(\int \frac{\sin ^{2} x-\cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x\) is equal to

1 \(\tan x+\cot x+c\)
2 \(\operatorname{cosec} x+\sec x+c\)
3 \(\tan x+\sec x+c\)
4 \(\tan x+\operatorname{cosec} x+c\)
AMU-2002
Integral Calculus

86275 \(\int\left(\frac{x-1}{x^{2}}\right) e^{x} d x\) is equal to

1 \(\mathrm{e}^{\mathrm{x}}+\frac{1}{\mathrm{x}}+\mathrm{c}\)
2 \(\frac{e^{x}}{x}+c\)
3 \(\frac{e^{x}}{x^{2}}+c\)
4 \(\mathrm{e}^{\mathrm{x}}\left(\log \mathrm{x}+\frac{1}{\mathrm{x}}\right)+\mathrm{c}\)
AMU-2002