Question

Calculo

Integração por parte

∫2x (x²+1)^4 dx

Answer 1

Olá

$\displaystyle\mathsf{\int 2x(x^2+1)^4dx}$


Fazendo a substituição udu

$\mathsf{u=x^2+1}\\\mathsf{du=2xdx}$

Substituindo na integral

$\displaystyle\mathsf{\int u^4 dx}\\\\\\\\= \mathsf{\frac{u^{4+1}}{4+1} }\\\\\\=\mathsf{ \frac{u^5}{5} +C}\\\\\\\text{Voltando com }x^2+1~\text{de volta no lugar do 'u'}\\\\\\= \boxed{\mathsf{\frac{(x^2+1)^5}{5} +C}}$