Question

$\int e^{3\log x}{(x^4+1)}^{-1}dx=$

Answer 1

$\int e^{3\log x}{(x^4+1)}^{-1}dx$

as $e^{loga}=a$

$\Rightarrow \int \frac{x^3}{(x^4+1)}dx$

$\Rightarrow$ Putting $x^4+1=m$

${4x}^{3}dx=dm$

$\Rightarrow \frac{1}{4}\int \frac{dm}{m}=\frac{1}{4}ln\left|m\right|+c=\frac{1}{4}ln[x^4+1]+c$