Question

The integral $\int \frac{2x^{12}+5x^9}{(x^5+x^3+1{)}^3}$ dx is equal to : where C is an arbitary constant.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$\int \frac{2x^{12}+5x^9}{x^2+x^3+1}dx=\int \frac{(\frac{2}{x^3}+\frac{5}{x^6})dx}{{(1+\frac{1}{x^2}+\frac{1}{x^5})}^3}1+\frac{1}{x^2}+\frac{1}{x^5}=t(-\frac{2}{x^3}-\frac{5}{x^6})dx=dt=\int \frac{-dt}{t^3}=\frac{1}{2t^2}+C\frac{1}{2{(1+\frac{1}{x^2}+\frac{1}{x^5})}^3}+C=\frac{x^{10}}{2(x^5+x^3+1{)}^2}+C$