Tổng hợp đầy đủ những công thức tích phân hàm vô tỉ không nên bỏ qua

\(\displaystyle \int \dfrac{dx}{\sqrt{ax+b}}= \dfrac{2}{a} \sqrt{ax+b} +C\)

\(\displaystyle \int \sqrt{ax+b}dx= \dfrac{2}{3a} (ax+b)^{\dfrac{3}{2}} +C\)

\(\displaystyle \int \dfrac{xdx}{\sqrt{ax+b}}= \dfrac{2(ax-2b)}{3a^2} \sqrt{ax+b} +C\)

\(\displaystyle \int x \sqrt{ax+b}dx= \dfrac{2(3ax-2b)}{15a^2} (ax+b)^{\dfrac{2}{3}} +C\)

\(\displaystyle \int \dfrac{dx}{(x+c)\sqrt{ax+b}}= \dfrac{1}{\sqrt{b-ac}} ln| \dfrac{ \sqrt{ax+b}- \sqrt{b-ac}}{ \sqrt{ax+b}+ \sqrt{b-ac}}| +C\)

\((ac-b>0)\)

\(\displaystyle \int \dfrac{dx}{(x+c)\sqrt{ax+b}}= \dfrac{1}{\sqrt{ac-b}} arctan \sqrt{\dfrac{ax+b}{ac-b}}C\)

\((ac-b)>0\)

\(\displaystyle \int x^2 \sqrt{a+bx}dx= \dfrac{2(8a^2-12abx+15b^2)\sqrt{(a+bx)^3}}{105b^3} +C\)

\(\displaystyle \int \dfrac{dx}{\sqrt{a^2+x^2}}= ln(x+ \sqrt{x^2+a^2}) + C\)

\(\displaystyle \int \dfrac{dx}{\sqrt{x^2-a^2}}= ln(x+ \sqrt{x^2-a^2}) + C\)

\(\displaystyle \int \dfrac{dx}{\sqrt{a^2-x^2}}= sin^{-1} \dfrac{x}{a} + C\)

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