Integration by Parts
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Integral Calculus

86308 \(\int \frac{d x}{(x-3)^{4 / 5}(x+1)^{6 / 5}}=\)

1 \(\frac{5}{4} \sqrt[5]{\frac{x-3}{x+1}}+C\)
2 \(\frac{5}{4}\left(\frac{x+1}{x-3}\right)^{1 / 5}+C\)
3 \(\frac{1}{5}\left(\frac{x-3}{x+1}\right)^{1 / 5}+C\)
4 \(\frac{5}{4}\left(\frac{\mathrm{x}-3}{\mathrm{x}+4}\right)^{4 / 5}+\mathrm{C}\)
AP EAMCET-2022-05.07.2022
Integral Calculus

86309 \(\int \frac{d x}{x^{3}+3 x^{2}+2 x}=\)

1 \(\log |x|+\log \left|\frac{x+2}{x+1}\right|+c\)
2 \(\log |\mathrm{x}|-\log |\mathrm{x}+1|+\log |\mathrm{x}+2|+\mathrm{c}\)
3 \(\frac{1}{2}[\log |\mathrm{x}|+\log |\mathrm{x}+1|+\log |\mathrm{x}+2|]+\mathrm{c}\)
4 \(\frac{1}{2} \log \left(\frac{\left|\mathrm{x}^{2}+2 \mathrm{x}\right|}{(\mathrm{x}+1)^{2}}\right)+\mathrm{c}\)
AP EAMCET-2018-22.04.2018
Integral Calculus

86310 \(\int x^{2020}\left(\tan ^{-1} x+\cot ^{-1} x\right) d x=\)

1 \(\frac{x^{2021}}{2020}\left(\tan ^{-1} x+\cot ^{-1} x\right)+c\)
2 \(\frac{x^{2021}}{2021}\left(\tan ^{-1} x+\cot ^{-1} x\right)+c\)
3 \(\frac{\pi \mathrm{x}^{2021}}{2021}+\frac{\pi}{2}+\mathrm{c}\)
4 \(\frac{\mathrm{x}^{52}}{52}+\frac{\pi}{2}+\mathrm{c}\)
AP EAMCET-2020-21.09.2020
Integral Calculus

86311 \(\int x\left(\tan ^{2} x\right) d x=\)

1 \(x \tan (\mathrm{x})-\log _{\mathrm{e}}(\sec \mathrm{x})-\frac{x^{2}}{2}+c\)
2 \(x \tan (x)+\log _{e}(\sec x)-\frac{x^{2}}{2}+c\)
3 \(x \tan (\mathrm{x})-\log _{\mathrm{e}}(\sec \mathrm{x})+\frac{x^{2}}{2}+c\)
4 \(x \tan (x)+\log _{e}(\sec x)+\frac{x^{2}}{2}+c\)
AP EAMCET-2020-21.09.2020
NEET DIGITAL LIBRARY
Integral Calculus

86308 \(\int \frac{d x}{(x-3)^{4 / 5}(x+1)^{6 / 5}}=\)

1 \(\frac{5}{4} \sqrt[5]{\frac{x-3}{x+1}}+C\)
2 \(\frac{5}{4}\left(\frac{x+1}{x-3}\right)^{1 / 5}+C\)
3 \(\frac{1}{5}\left(\frac{x-3}{x+1}\right)^{1 / 5}+C\)
4 \(\frac{5}{4}\left(\frac{\mathrm{x}-3}{\mathrm{x}+4}\right)^{4 / 5}+\mathrm{C}\)
AP EAMCET-2022-05.07.2022
Integral Calculus

86309 \(\int \frac{d x}{x^{3}+3 x^{2}+2 x}=\)

1 \(\log |x|+\log \left|\frac{x+2}{x+1}\right|+c\)
2 \(\log |\mathrm{x}|-\log |\mathrm{x}+1|+\log |\mathrm{x}+2|+\mathrm{c}\)
3 \(\frac{1}{2}[\log |\mathrm{x}|+\log |\mathrm{x}+1|+\log |\mathrm{x}+2|]+\mathrm{c}\)
4 \(\frac{1}{2} \log \left(\frac{\left|\mathrm{x}^{2}+2 \mathrm{x}\right|}{(\mathrm{x}+1)^{2}}\right)+\mathrm{c}\)
AP EAMCET-2018-22.04.2018
Integral Calculus

86310 \(\int x^{2020}\left(\tan ^{-1} x+\cot ^{-1} x\right) d x=\)

1 \(\frac{x^{2021}}{2020}\left(\tan ^{-1} x+\cot ^{-1} x\right)+c\)
2 \(\frac{x^{2021}}{2021}\left(\tan ^{-1} x+\cot ^{-1} x\right)+c\)
3 \(\frac{\pi \mathrm{x}^{2021}}{2021}+\frac{\pi}{2}+\mathrm{c}\)
4 \(\frac{\mathrm{x}^{52}}{52}+\frac{\pi}{2}+\mathrm{c}\)
AP EAMCET-2020-21.09.2020
Integral Calculus

86311 \(\int x\left(\tan ^{2} x\right) d x=\)

1 \(x \tan (\mathrm{x})-\log _{\mathrm{e}}(\sec \mathrm{x})-\frac{x^{2}}{2}+c\)
2 \(x \tan (x)+\log _{e}(\sec x)-\frac{x^{2}}{2}+c\)
3 \(x \tan (\mathrm{x})-\log _{\mathrm{e}}(\sec \mathrm{x})+\frac{x^{2}}{2}+c\)
4 \(x \tan (x)+\log _{e}(\sec x)+\frac{x^{2}}{2}+c\)
AP EAMCET-2020-21.09.2020
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Integral Calculus

86308 \(\int \frac{d x}{(x-3)^{4 / 5}(x+1)^{6 / 5}}=\)

1 \(\frac{5}{4} \sqrt[5]{\frac{x-3}{x+1}}+C\)
2 \(\frac{5}{4}\left(\frac{x+1}{x-3}\right)^{1 / 5}+C\)
3 \(\frac{1}{5}\left(\frac{x-3}{x+1}\right)^{1 / 5}+C\)
4 \(\frac{5}{4}\left(\frac{\mathrm{x}-3}{\mathrm{x}+4}\right)^{4 / 5}+\mathrm{C}\)
AP EAMCET-2022-05.07.2022
Integral Calculus

86309 \(\int \frac{d x}{x^{3}+3 x^{2}+2 x}=\)

1 \(\log |x|+\log \left|\frac{x+2}{x+1}\right|+c\)
2 \(\log |\mathrm{x}|-\log |\mathrm{x}+1|+\log |\mathrm{x}+2|+\mathrm{c}\)
3 \(\frac{1}{2}[\log |\mathrm{x}|+\log |\mathrm{x}+1|+\log |\mathrm{x}+2|]+\mathrm{c}\)
4 \(\frac{1}{2} \log \left(\frac{\left|\mathrm{x}^{2}+2 \mathrm{x}\right|}{(\mathrm{x}+1)^{2}}\right)+\mathrm{c}\)
AP EAMCET-2018-22.04.2018
Integral Calculus

86310 \(\int x^{2020}\left(\tan ^{-1} x+\cot ^{-1} x\right) d x=\)

1 \(\frac{x^{2021}}{2020}\left(\tan ^{-1} x+\cot ^{-1} x\right)+c\)
2 \(\frac{x^{2021}}{2021}\left(\tan ^{-1} x+\cot ^{-1} x\right)+c\)
3 \(\frac{\pi \mathrm{x}^{2021}}{2021}+\frac{\pi}{2}+\mathrm{c}\)
4 \(\frac{\mathrm{x}^{52}}{52}+\frac{\pi}{2}+\mathrm{c}\)
AP EAMCET-2020-21.09.2020
Integral Calculus

86311 \(\int x\left(\tan ^{2} x\right) d x=\)

1 \(x \tan (\mathrm{x})-\log _{\mathrm{e}}(\sec \mathrm{x})-\frac{x^{2}}{2}+c\)
2 \(x \tan (x)+\log _{e}(\sec x)-\frac{x^{2}}{2}+c\)
3 \(x \tan (\mathrm{x})-\log _{\mathrm{e}}(\sec \mathrm{x})+\frac{x^{2}}{2}+c\)
4 \(x \tan (x)+\log _{e}(\sec x)+\frac{x^{2}}{2}+c\)
AP EAMCET-2020-21.09.2020
For More Updates join with Us
Integral Calculus

86308 \(\int \frac{d x}{(x-3)^{4 / 5}(x+1)^{6 / 5}}=\)

1 \(\frac{5}{4} \sqrt[5]{\frac{x-3}{x+1}}+C\)
2 \(\frac{5}{4}\left(\frac{x+1}{x-3}\right)^{1 / 5}+C\)
3 \(\frac{1}{5}\left(\frac{x-3}{x+1}\right)^{1 / 5}+C\)
4 \(\frac{5}{4}\left(\frac{\mathrm{x}-3}{\mathrm{x}+4}\right)^{4 / 5}+\mathrm{C}\)
AP EAMCET-2022-05.07.2022
Integral Calculus

86309 \(\int \frac{d x}{x^{3}+3 x^{2}+2 x}=\)

1 \(\log |x|+\log \left|\frac{x+2}{x+1}\right|+c\)
2 \(\log |\mathrm{x}|-\log |\mathrm{x}+1|+\log |\mathrm{x}+2|+\mathrm{c}\)
3 \(\frac{1}{2}[\log |\mathrm{x}|+\log |\mathrm{x}+1|+\log |\mathrm{x}+2|]+\mathrm{c}\)
4 \(\frac{1}{2} \log \left(\frac{\left|\mathrm{x}^{2}+2 \mathrm{x}\right|}{(\mathrm{x}+1)^{2}}\right)+\mathrm{c}\)
AP EAMCET-2018-22.04.2018
Integral Calculus

86310 \(\int x^{2020}\left(\tan ^{-1} x+\cot ^{-1} x\right) d x=\)

1 \(\frac{x^{2021}}{2020}\left(\tan ^{-1} x+\cot ^{-1} x\right)+c\)
2 \(\frac{x^{2021}}{2021}\left(\tan ^{-1} x+\cot ^{-1} x\right)+c\)
3 \(\frac{\pi \mathrm{x}^{2021}}{2021}+\frac{\pi}{2}+\mathrm{c}\)
4 \(\frac{\mathrm{x}^{52}}{52}+\frac{\pi}{2}+\mathrm{c}\)
AP EAMCET-2020-21.09.2020
Integral Calculus

86311 \(\int x\left(\tan ^{2} x\right) d x=\)

1 \(x \tan (\mathrm{x})-\log _{\mathrm{e}}(\sec \mathrm{x})-\frac{x^{2}}{2}+c\)
2 \(x \tan (x)+\log _{e}(\sec x)-\frac{x^{2}}{2}+c\)
3 \(x \tan (\mathrm{x})-\log _{\mathrm{e}}(\sec \mathrm{x})+\frac{x^{2}}{2}+c\)
4 \(x \tan (x)+\log _{e}(\sec x)+\frac{x^{2}}{2}+c\)
AP EAMCET-2020-21.09.2020
NEET DIGITAL LIBRARY