Question

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

• A. $\frac{5}{11}(x^2+2x{)}^{11/10}+c$
• B. $\frac{5}{6}(x+1{)}^{11/10}+c$
• C. $\frac{6}{7}(x+1{)}^{11/10}+c$
• D. None of these

Answer 1

The correct option is A

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

$\int (x^2+x)(x^{-8}+2x^{-9}{)}^{1/10}dx=\int (x+1\left)\right(x^2+2x{)}^{1/10}dx$
Now put $x^2+2x=t\Rightarrow (x+1)dx=\frac{dt}{2}$
$\Rightarrow \int t^{1/10}.\frac{dt}{2}=\frac{1}{2}\times \frac{10}{11}{t}^{11/10}=\frac{5}{11}{t}^{11/10}+c$
$\Rightarrow \frac{5}{11}(x^2+2x{)}^{11/10}+c$