The integral $\int \frac{3 x^{13}+2 x^{11}}{\left(2 x^4+3 x^2+1\right)^4} d x$ is equal to (where $C$ is a constant of integration.)

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Aicharya · Accepted Answer

$\begin{aligned} & \int \frac{3 x^{13}+2 x^{11}}{\left(2 x^4+3 x^2+1ight)^4} d x=\int \frac{3 x^{13}+2 x^{11}}{x^{16}\left(2+\frac{3}{x^2}+\frac{1}{x^4}ight)^4} d x \ & =-\frac{1}{2} \int \frac{-6 x^{-3}-4 x^{-5}}{\left(2+\frac{3}{x^2}+\frac{1}{x^4}ight)^4} d x=\frac{-1}{2} 	imes \frac{-1}{3}\left(2+\frac{3}{x^2}+\frac{1}{x^4}ight)^{-3}+C \ & =\frac{1}{6}\left(\frac{2 x^4+3 x^2+1}{x^4}ight)^{-3}+C=\frac{x^{12}}{6\left(2 x^4+3 x^2+1ight)^3}+C\end{aligned}$

The integral $\int \frac{3 x^{13}+2 x^{11}}{\left(2 x^4+3 x^2+1\right)^4} d x$ is equal to (where $C$ is a…

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