Integration by Parts
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Integral Calculus

86282 \(\int \frac{x-1}{(x-2)(x-3)} d x=\)

1 \(2 \log |\mathrm{x}-3|+\log |\mathrm{x}-2|+\mathrm{c} 2\)
2 \(2 \log |\mathrm{x}-3|-\log |\mathrm{x}-2|+\mathrm{c}\)
3 \(2 \log |\mathrm{x}-3|+\log |\mathrm{x}-2|+\mathrm{c}\)
4 \(\log \left|\frac{(\mathrm{x}-3)^{2}}{\mathrm{x}-2}\right|+\mathrm{c}\)
Shift-II]
Integral Calculus

86283 If \(\int e^{x}\left(\frac{x+2}{x+4}\right)^{2} d x=f(x)+\) arbitrary constant, then \(\mathbf{f}(\mathbf{x})=\)

1 \(\frac{x e^{x}}{x+4}\)
2 \(\frac{e^{x}}{x+4}\)
3 \(\frac{\mathrm{xe}^{\mathrm{x}}}{(\mathrm{x}+4)^{2}}\)
4 \(\frac{e^{x}}{(x+4)^{2}}\)
AP EAMCET-2019-21.04.2019
Integral Calculus

86219 \(\int \sqrt{x} e^{\sqrt{x}} d x\) is equal to :

1 \(2 \sqrt{x}-e^{\sqrt{x}}-4 \sqrt{x e^{\sqrt{x}}}+C\)
2 \((2 x-4 \sqrt{x}+4) e^{\sqrt{x}}+C\)
3 \((2 x+4 \sqrt{x}+4) e^{\sqrt{x}}+C\)
4 \((1-4 \sqrt{x}) e^{\sqrt{x}}+C\)
Karnataka CET-2004
Integral Calculus

86222 The value of \(\int \frac{e^{x}(1+x) d x}{\cos ^{2}\left(e^{x} \cdot x\right)}\) is equal to

1 \(-\cot \left(\mathrm{e}^{\mathrm{x}} \cdot \mathrm{x}\right)+\mathrm{C}\)
2 \(\tan \left(\mathrm{e}^{\mathrm{x}} \cdot \mathrm{x}\right)+\mathrm{C}\)
3 \(\tan \left(\mathrm{e}^{\mathrm{x}}\right)+\mathrm{C}\)
4 \(\cot \left(\mathrm{e}^{\mathrm{x}}\right)+\mathrm{C}\)
Karnataka CET-2016
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Integral Calculus

86282 \(\int \frac{x-1}{(x-2)(x-3)} d x=\)

1 \(2 \log |\mathrm{x}-3|+\log |\mathrm{x}-2|+\mathrm{c} 2\)
2 \(2 \log |\mathrm{x}-3|-\log |\mathrm{x}-2|+\mathrm{c}\)
3 \(2 \log |\mathrm{x}-3|+\log |\mathrm{x}-2|+\mathrm{c}\)
4 \(\log \left|\frac{(\mathrm{x}-3)^{2}}{\mathrm{x}-2}\right|+\mathrm{c}\)
Shift-II]
Integral Calculus

86283 If \(\int e^{x}\left(\frac{x+2}{x+4}\right)^{2} d x=f(x)+\) arbitrary constant, then \(\mathbf{f}(\mathbf{x})=\)

1 \(\frac{x e^{x}}{x+4}\)
2 \(\frac{e^{x}}{x+4}\)
3 \(\frac{\mathrm{xe}^{\mathrm{x}}}{(\mathrm{x}+4)^{2}}\)
4 \(\frac{e^{x}}{(x+4)^{2}}\)
AP EAMCET-2019-21.04.2019
Integral Calculus

86219 \(\int \sqrt{x} e^{\sqrt{x}} d x\) is equal to :

1 \(2 \sqrt{x}-e^{\sqrt{x}}-4 \sqrt{x e^{\sqrt{x}}}+C\)
2 \((2 x-4 \sqrt{x}+4) e^{\sqrt{x}}+C\)
3 \((2 x+4 \sqrt{x}+4) e^{\sqrt{x}}+C\)
4 \((1-4 \sqrt{x}) e^{\sqrt{x}}+C\)
Karnataka CET-2004
Integral Calculus

86222 The value of \(\int \frac{e^{x}(1+x) d x}{\cos ^{2}\left(e^{x} \cdot x\right)}\) is equal to

1 \(-\cot \left(\mathrm{e}^{\mathrm{x}} \cdot \mathrm{x}\right)+\mathrm{C}\)
2 \(\tan \left(\mathrm{e}^{\mathrm{x}} \cdot \mathrm{x}\right)+\mathrm{C}\)
3 \(\tan \left(\mathrm{e}^{\mathrm{x}}\right)+\mathrm{C}\)
4 \(\cot \left(\mathrm{e}^{\mathrm{x}}\right)+\mathrm{C}\)
Karnataka CET-2016
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Integral Calculus

86282 \(\int \frac{x-1}{(x-2)(x-3)} d x=\)

1 \(2 \log |\mathrm{x}-3|+\log |\mathrm{x}-2|+\mathrm{c} 2\)
2 \(2 \log |\mathrm{x}-3|-\log |\mathrm{x}-2|+\mathrm{c}\)
3 \(2 \log |\mathrm{x}-3|+\log |\mathrm{x}-2|+\mathrm{c}\)
4 \(\log \left|\frac{(\mathrm{x}-3)^{2}}{\mathrm{x}-2}\right|+\mathrm{c}\)
Shift-II]
Integral Calculus

86283 If \(\int e^{x}\left(\frac{x+2}{x+4}\right)^{2} d x=f(x)+\) arbitrary constant, then \(\mathbf{f}(\mathbf{x})=\)

1 \(\frac{x e^{x}}{x+4}\)
2 \(\frac{e^{x}}{x+4}\)
3 \(\frac{\mathrm{xe}^{\mathrm{x}}}{(\mathrm{x}+4)^{2}}\)
4 \(\frac{e^{x}}{(x+4)^{2}}\)
AP EAMCET-2019-21.04.2019
Integral Calculus

86219 \(\int \sqrt{x} e^{\sqrt{x}} d x\) is equal to :

1 \(2 \sqrt{x}-e^{\sqrt{x}}-4 \sqrt{x e^{\sqrt{x}}}+C\)
2 \((2 x-4 \sqrt{x}+4) e^{\sqrt{x}}+C\)
3 \((2 x+4 \sqrt{x}+4) e^{\sqrt{x}}+C\)
4 \((1-4 \sqrt{x}) e^{\sqrt{x}}+C\)
Karnataka CET-2004
Integral Calculus

86222 The value of \(\int \frac{e^{x}(1+x) d x}{\cos ^{2}\left(e^{x} \cdot x\right)}\) is equal to

1 \(-\cot \left(\mathrm{e}^{\mathrm{x}} \cdot \mathrm{x}\right)+\mathrm{C}\)
2 \(\tan \left(\mathrm{e}^{\mathrm{x}} \cdot \mathrm{x}\right)+\mathrm{C}\)
3 \(\tan \left(\mathrm{e}^{\mathrm{x}}\right)+\mathrm{C}\)
4 \(\cot \left(\mathrm{e}^{\mathrm{x}}\right)+\mathrm{C}\)
Karnataka CET-2016
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Integral Calculus

86282 \(\int \frac{x-1}{(x-2)(x-3)} d x=\)

1 \(2 \log |\mathrm{x}-3|+\log |\mathrm{x}-2|+\mathrm{c} 2\)
2 \(2 \log |\mathrm{x}-3|-\log |\mathrm{x}-2|+\mathrm{c}\)
3 \(2 \log |\mathrm{x}-3|+\log |\mathrm{x}-2|+\mathrm{c}\)
4 \(\log \left|\frac{(\mathrm{x}-3)^{2}}{\mathrm{x}-2}\right|+\mathrm{c}\)
Shift-II]
Integral Calculus

86283 If \(\int e^{x}\left(\frac{x+2}{x+4}\right)^{2} d x=f(x)+\) arbitrary constant, then \(\mathbf{f}(\mathbf{x})=\)

1 \(\frac{x e^{x}}{x+4}\)
2 \(\frac{e^{x}}{x+4}\)
3 \(\frac{\mathrm{xe}^{\mathrm{x}}}{(\mathrm{x}+4)^{2}}\)
4 \(\frac{e^{x}}{(x+4)^{2}}\)
AP EAMCET-2019-21.04.2019
Integral Calculus

86219 \(\int \sqrt{x} e^{\sqrt{x}} d x\) is equal to :

1 \(2 \sqrt{x}-e^{\sqrt{x}}-4 \sqrt{x e^{\sqrt{x}}}+C\)
2 \((2 x-4 \sqrt{x}+4) e^{\sqrt{x}}+C\)
3 \((2 x+4 \sqrt{x}+4) e^{\sqrt{x}}+C\)
4 \((1-4 \sqrt{x}) e^{\sqrt{x}}+C\)
Karnataka CET-2004
Integral Calculus

86222 The value of \(\int \frac{e^{x}(1+x) d x}{\cos ^{2}\left(e^{x} \cdot x\right)}\) is equal to

1 \(-\cot \left(\mathrm{e}^{\mathrm{x}} \cdot \mathrm{x}\right)+\mathrm{C}\)
2 \(\tan \left(\mathrm{e}^{\mathrm{x}} \cdot \mathrm{x}\right)+\mathrm{C}\)
3 \(\tan \left(\mathrm{e}^{\mathrm{x}}\right)+\mathrm{C}\)
4 \(\cot \left(\mathrm{e}^{\mathrm{x}}\right)+\mathrm{C}\)
Karnataka CET-2016