Tổng hợp những phương pháp đổi hàm tích phân học sinh không nên bỏ qua

\(\displaystyle \int F(ax+b)dx = \dfrac{1}{a} \displaystyle \int F(u)du, u =ax+b\)

\(\displaystyle \int F(\sqrt{ax+b})dx = \dfrac{2}{a} \displaystyle \int uF(u)du, u =\sqrt{ax+b}\)

\(\displaystyle \int F(^n\sqrt{ax+b})dx = \dfrac{n}{a} \displaystyle \int u^{n-1}F(u)du, u =^n\sqrt{ax+b}\)

\(\displaystyle \int F(\sqrt{a^2-x^2})dx = a \displaystyle \int F(acosu)\ cosu \ du, x=a \ sinu\)

\(\displaystyle \int F(\sqrt{a^2+x^2})dx = a \displaystyle \int F(a\ secu)\ sec^2u \ du, x=a \ tanu\)

\(\displaystyle \int F(\sqrt{x^2-a^2})dx = a \displaystyle \int F(a\ tanu)\ secu \ tan u \ du, x=a \ secu\)

\(\displaystyle \int F(e^{ax})dx = \dfrac{1}{a} \displaystyle \int \dfrac{F(u)}{u} du, u =e^{ax}\)

\(\displaystyle \int F(lnx)dx = \displaystyle \int F(u)e^u du, u =lnx\)