Giải thích các bước giải:
$A=\int \dfrac{x^3-2x}{\sqrt{x^2+1}}dx$
$=\int \dfrac{x(x^2-2)}{\sqrt{x^2+1}}dx$
$=\int \dfrac{2x(x^2-2)}{2\sqrt{x^2+1}}dx$
$=\int \dfrac{x^2-2}{2\sqrt{x^2+1}}d(x^2)$
$=\int \dfrac{x^2-2}{2\sqrt{x^2+1}}d(x^2+1)$
Đặt $x^2+1=y$
$\rightarrow A=\int \dfrac{y-3}{2\sqrt{y}}dy$
$\rightarrow A=\int \dfrac{1}{2}y^\dfrac{1}{2}-\dfrac{3}{2\sqrt{y}}dy$
$\rightarrow A= \dfrac{1}{2}.\dfrac{2}{3}y^\dfrac{3}{2}-3\sqrt{y}$
$\rightarrow A= \dfrac{1}{3}y^\dfrac{3}{2}-3\sqrt{y}$
$\rightarrow A= \dfrac{1}{3}(x^2+1)^\dfrac{3}{2}-3\sqrt{x^2+1}$
