The value of ∫x2+xx−8+2x−9110dx is

∫x2+xx−8+2x−9110dx =∫x +1xx−8+2x−9110dx =∫x+1x10x−8+2x−9110dx =∫(x+1)x2+2x110dx =12x2+2x11101110=511x2+2x1110+c

The value of ∫x2+xx−8+2x−9110dx is

∫x2+xx−8+2x−9110dx =∫x +1xx−8+2x−9110dx =∫x+1x10x−8+2x−9110dx =∫(x+1)x2+2x110dx =12x2+2x11101110=511x2+2x1110+c

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The value of $\int (x^{2} + x) {(x^{- 8} + 2 x^{- 9})}^{\frac{1}{10}} dx$ is

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$\frac{5}{6} (x + 1)^{\frac{11}{10}} + c$

$\frac{6}{7} (x + 1)^{\frac{11}{10}} + c$

$\frac{5}{11} {(x^{2} + 2 x)}^{\frac{11}{10}} + c$

$\frac{3}{5} (x + 1)^{\frac{11}{10}} + c$

answer is A.

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Detailed Solution

$\int (x^{2} + x) {(x^{- 8} + 2 x^{- 9})}^{\frac{1}{10}} dx = \int (x^{} + 1) x {(x^{- 8} + 2 x^{- 9})}^{\frac{1}{10}} dx = \int (x + 1) {[x^{10} (x^{- 8} + 2 x^{- 9})]}^{\frac{1}{10}} dx = \int (x + 1) {(x^{2} + 2 x)}^{\frac{1}{10}} dx = \frac{1}{2} \frac{{(x^{2} + 2 x)}^{\frac{11}{10}}}{\frac{11}{10}} = \frac{5}{11} {(x^{2} + 2 x)}^{\frac{11}{10}} + c$