Giải thích các bước giải:
Ta có:
$A=\int \dfrac{x^3}{2x^2+1}dx$
$\rightarrow A=\int \dfrac{1}{2}\dfrac{x(2x^2+1-1)}{2x^2+1}dx$
$\rightarrow A=\int \dfrac{1}{2}\dfrac{x(2x^2+1)-x)}{2x^2+1}dx$
$\rightarrow A=\int \dfrac{1}{2}(x-\dfrac{x}{2x^2+1})dx$
$\rightarrow A=\int \dfrac{1}{2}(x-\dfrac{1}{2}\dfrac{2x}{2x^2+1})dx$
$\rightarrow A=\dfrac{1}{2}.(\dfrac{x^2}{2}-\dfrac{1}{2}.ln(2x^2+1))+C$
$\rightarrow \int^2_0 \dfrac{x^3}{2x^2+1}dx=\dfrac{1}{2}(2-\dfrac{1}{2}.ln5)$
