Giải thích các bước giải:
Ta có:
$I=\displaystyle\int\dfrac{x^5}{x^2+1}dx$
Đặt $x^2=t\to dx^2=dt\to 2xdx=dt$
$\to I=\dfrac12\displaystyle\int\dfrac{x^4}{x^2+1}\cdot 2xdx$
$\to I=\dfrac12\displaystyle\int\dfrac{t^2}{t+1} dt$
$\to I=\dfrac12\displaystyle\int\dfrac{t^2-1+1}{t+1} dt$
$\to I=\dfrac12\displaystyle\int\dfrac{(t-1)(t+1)+1}{t+1} dt$
$\to I=\dfrac12\displaystyle\int(t-1+\dfrac{1}{t+1}) dt$
$\to I=\dfrac12(\dfrac12t^2-t+\ln|t+1|)$
$\to I=\dfrac12(\dfrac12x^4-x^2+\ln|x^2+1|)$
