Integration by Parts
« Previous Topic: Integrations and Integration of Functions Next Topic: Definite Integral as Limit of a Sum »
Join With Us for More Updates
Integral Calculus

86357 \(\int \mathrm{e}^{3 \log \mathrm{x}}\left(\mathrm{x}^{4}+1\right)^{-1} \mathrm{dx}\) is equal to

1 \(\mathrm{e}^{3 \log \mathrm{x}}+\mathrm{C}\)
2 \(\frac{1}{4} \log \left(\mathrm{x}^{4}+1\right)+\mathrm{C}\)
3 \(\log \left(\mathrm{x}^{4}+1\right)+\mathrm{C}\)
4 \(\frac{1}{2} \log \left(\mathrm{x}^{4}+1\right)+\mathrm{C}\)
5 \(\frac{\mathrm{x}^{4}}{\mathrm{x}^{4}+1}+\mathrm{C}\)
Kerala CEE-2008
Integral Calculus

86358 \(\int(\sin x-\cos x)^{4}(\sin x+\cos x) d x\) is equal to

1 \(\frac{\sin x-\cos x}{5}+C\)
2 \(\frac{(\sin x-\cos x)^{5}}{5}+C\)
3 \(\frac{(\sin x-\cos x)^{4}}{4}+C\)
4 \(\frac{(\sin x+\cos x)^{5}}{5}+C\)
5 None of the above
Kerala CEE-2008
Integral Calculus

86359 If \(f(x)=\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}\) and \(g(x)=\mathrm{e}^{\sin ^{-1} x}\), then \(\int f(x) g(x)\) is equal to

1 \(\mathrm{e}^{\sin ^{-1} x}\left(\sin ^{-1} x-1\right)+C\)
2 \(\mathrm{e}^{\sin ^{-1} x}+\mathrm{C}\)
3 \(\mathrm{e}^{\left(\sin ^{-1} x\right)^{2}}+\mathrm{C}\)
4 \(\mathrm{e}^{2 \sin ^{-1} x}+C\)
5 \(\mathrm{e}^{\sin ^{-1} x} \sin ^{-1} x+C\)
Kerala CEE-2007
Integral Calculus

86360 \(\int e^{x}\{\log \sin x+\cot x\} d x\) is equal to :

1 \(e^{x} \cot x+C\)
2 \(e^{x} \log \sin x+C\)
3 \(\mathrm{e}^{\mathrm{x}} \log \sin \mathrm{x}+\tan \mathrm{x}+\mathrm{C}\)
4 \(\mathrm{e}^{\mathrm{x}}+\sin \mathrm{x}+\mathrm{C}\)
5 \(\log (\sin \mathrm{x}+\cos \mathrm{x})+\mathrm{e}^{\mathrm{x}}+C\)
Kerala CEE-2006
For More Updates join with Us
Integral Calculus

86357 \(\int \mathrm{e}^{3 \log \mathrm{x}}\left(\mathrm{x}^{4}+1\right)^{-1} \mathrm{dx}\) is equal to

1 \(\mathrm{e}^{3 \log \mathrm{x}}+\mathrm{C}\)
2 \(\frac{1}{4} \log \left(\mathrm{x}^{4}+1\right)+\mathrm{C}\)
3 \(\log \left(\mathrm{x}^{4}+1\right)+\mathrm{C}\)
4 \(\frac{1}{2} \log \left(\mathrm{x}^{4}+1\right)+\mathrm{C}\)
5 \(\frac{\mathrm{x}^{4}}{\mathrm{x}^{4}+1}+\mathrm{C}\)
Kerala CEE-2008
Integral Calculus

86358 \(\int(\sin x-\cos x)^{4}(\sin x+\cos x) d x\) is equal to

1 \(\frac{\sin x-\cos x}{5}+C\)
2 \(\frac{(\sin x-\cos x)^{5}}{5}+C\)
3 \(\frac{(\sin x-\cos x)^{4}}{4}+C\)
4 \(\frac{(\sin x+\cos x)^{5}}{5}+C\)
5 None of the above
Kerala CEE-2008
Integral Calculus

86359 If \(f(x)=\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}\) and \(g(x)=\mathrm{e}^{\sin ^{-1} x}\), then \(\int f(x) g(x)\) is equal to

1 \(\mathrm{e}^{\sin ^{-1} x}\left(\sin ^{-1} x-1\right)+C\)
2 \(\mathrm{e}^{\sin ^{-1} x}+\mathrm{C}\)
3 \(\mathrm{e}^{\left(\sin ^{-1} x\right)^{2}}+\mathrm{C}\)
4 \(\mathrm{e}^{2 \sin ^{-1} x}+C\)
5 \(\mathrm{e}^{\sin ^{-1} x} \sin ^{-1} x+C\)
Kerala CEE-2007
Integral Calculus

86360 \(\int e^{x}\{\log \sin x+\cot x\} d x\) is equal to :

1 \(e^{x} \cot x+C\)
2 \(e^{x} \log \sin x+C\)
3 \(\mathrm{e}^{\mathrm{x}} \log \sin \mathrm{x}+\tan \mathrm{x}+\mathrm{C}\)
4 \(\mathrm{e}^{\mathrm{x}}+\sin \mathrm{x}+\mathrm{C}\)
5 \(\log (\sin \mathrm{x}+\cos \mathrm{x})+\mathrm{e}^{\mathrm{x}}+C\)
Kerala CEE-2006
NEET DIGITAL LIBRARY
Integral Calculus

86357 \(\int \mathrm{e}^{3 \log \mathrm{x}}\left(\mathrm{x}^{4}+1\right)^{-1} \mathrm{dx}\) is equal to

1 \(\mathrm{e}^{3 \log \mathrm{x}}+\mathrm{C}\)
2 \(\frac{1}{4} \log \left(\mathrm{x}^{4}+1\right)+\mathrm{C}\)
3 \(\log \left(\mathrm{x}^{4}+1\right)+\mathrm{C}\)
4 \(\frac{1}{2} \log \left(\mathrm{x}^{4}+1\right)+\mathrm{C}\)
5 \(\frac{\mathrm{x}^{4}}{\mathrm{x}^{4}+1}+\mathrm{C}\)
Kerala CEE-2008
Integral Calculus

86358 \(\int(\sin x-\cos x)^{4}(\sin x+\cos x) d x\) is equal to

1 \(\frac{\sin x-\cos x}{5}+C\)
2 \(\frac{(\sin x-\cos x)^{5}}{5}+C\)
3 \(\frac{(\sin x-\cos x)^{4}}{4}+C\)
4 \(\frac{(\sin x+\cos x)^{5}}{5}+C\)
5 None of the above
Kerala CEE-2008
Integral Calculus

86359 If \(f(x)=\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}\) and \(g(x)=\mathrm{e}^{\sin ^{-1} x}\), then \(\int f(x) g(x)\) is equal to

1 \(\mathrm{e}^{\sin ^{-1} x}\left(\sin ^{-1} x-1\right)+C\)
2 \(\mathrm{e}^{\sin ^{-1} x}+\mathrm{C}\)
3 \(\mathrm{e}^{\left(\sin ^{-1} x\right)^{2}}+\mathrm{C}\)
4 \(\mathrm{e}^{2 \sin ^{-1} x}+C\)
5 \(\mathrm{e}^{\sin ^{-1} x} \sin ^{-1} x+C\)
Kerala CEE-2007
Integral Calculus

86360 \(\int e^{x}\{\log \sin x+\cot x\} d x\) is equal to :

1 \(e^{x} \cot x+C\)
2 \(e^{x} \log \sin x+C\)
3 \(\mathrm{e}^{\mathrm{x}} \log \sin \mathrm{x}+\tan \mathrm{x}+\mathrm{C}\)
4 \(\mathrm{e}^{\mathrm{x}}+\sin \mathrm{x}+\mathrm{C}\)
5 \(\log (\sin \mathrm{x}+\cos \mathrm{x})+\mathrm{e}^{\mathrm{x}}+C\)
Kerala CEE-2006
Join With Us for More Updates
Integral Calculus

86357 \(\int \mathrm{e}^{3 \log \mathrm{x}}\left(\mathrm{x}^{4}+1\right)^{-1} \mathrm{dx}\) is equal to

1 \(\mathrm{e}^{3 \log \mathrm{x}}+\mathrm{C}\)
2 \(\frac{1}{4} \log \left(\mathrm{x}^{4}+1\right)+\mathrm{C}\)
3 \(\log \left(\mathrm{x}^{4}+1\right)+\mathrm{C}\)
4 \(\frac{1}{2} \log \left(\mathrm{x}^{4}+1\right)+\mathrm{C}\)
5 \(\frac{\mathrm{x}^{4}}{\mathrm{x}^{4}+1}+\mathrm{C}\)
Kerala CEE-2008
Integral Calculus

86358 \(\int(\sin x-\cos x)^{4}(\sin x+\cos x) d x\) is equal to

1 \(\frac{\sin x-\cos x}{5}+C\)
2 \(\frac{(\sin x-\cos x)^{5}}{5}+C\)
3 \(\frac{(\sin x-\cos x)^{4}}{4}+C\)
4 \(\frac{(\sin x+\cos x)^{5}}{5}+C\)
5 None of the above
Kerala CEE-2008
Integral Calculus

86359 If \(f(x)=\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}\) and \(g(x)=\mathrm{e}^{\sin ^{-1} x}\), then \(\int f(x) g(x)\) is equal to

1 \(\mathrm{e}^{\sin ^{-1} x}\left(\sin ^{-1} x-1\right)+C\)
2 \(\mathrm{e}^{\sin ^{-1} x}+\mathrm{C}\)
3 \(\mathrm{e}^{\left(\sin ^{-1} x\right)^{2}}+\mathrm{C}\)
4 \(\mathrm{e}^{2 \sin ^{-1} x}+C\)
5 \(\mathrm{e}^{\sin ^{-1} x} \sin ^{-1} x+C\)
Kerala CEE-2007
Integral Calculus

86360 \(\int e^{x}\{\log \sin x+\cot x\} d x\) is equal to :

1 \(e^{x} \cot x+C\)
2 \(e^{x} \log \sin x+C\)
3 \(\mathrm{e}^{\mathrm{x}} \log \sin \mathrm{x}+\tan \mathrm{x}+\mathrm{C}\)
4 \(\mathrm{e}^{\mathrm{x}}+\sin \mathrm{x}+\mathrm{C}\)
5 \(\log (\sin \mathrm{x}+\cos \mathrm{x})+\mathrm{e}^{\mathrm{x}}+C\)
Kerala CEE-2006
For More Updates join with Us