Question

Answer 1

Lời giải:

\(\int (x^2+3)^2\frac{d(x^2+3)}{2x}=\int (x^4+6x^2+9).\frac{2xdx}{2x}=\int (x^4+6x^2+9)dx\)

\(=\frac{x^5}{5}+2x^3+9x+C\)

Answer 2

\(A=\int\left(x^2+3\right)^2.\dfrac{d\left(x^2+3\right)}{2x}\left(1\right)\)

Đặt \(u=x^2+3\Rightarrow du=2xdx\)

\(\left(1\right)\Rightarrow A=\int u^2du=\dfrac{1}{3}u^3+C\)

\(\Rightarrow A=\int\left(x^2+3\right)^2.\dfrac{d\left(x^2+3\right)}{2x}=\dfrac{1}{3}\left(x^2+3\right)^3+C\)