$\int e^{3 \log x}\left(x^4+1\right)^{-1} d x$ is equal
Answer & explanation
Correct answer: option 2
We have,
$I =\int e^{3 \log x}\left(x^4+1\right)^{-1} d x=\int \frac{e^{\log x^3}}{x^4+1} d x=\int \frac{x^3}{x^4+1} d x$
$\Rightarrow I =\frac{1}{4} \int \frac{1}{x^4+1} d\left(x^4+1\right)=\frac{1}{4} \log \left(x^4+1\right)+C$