Đầy đủ những công thức tích phân hàm hữu tỉ học sinh không nên bỏ qua

\(\displaystyle \int \dfrac{dx}{x}= ln|x| + C\)

\(\displaystyle \int \dfrac{dx}{ax+b}=\dfrac{1}{a} ln|ax+b| + C\)

\(\displaystyle \int \dfrac{ax+b}{cx+d}dx= \dfrac{a}{c}x+ \dfrac{bc-ad}{c^2}ln|cx+d| + C\)

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

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

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

\(\displaystyle \int \dfrac{dx}{(x+a)(x+b)}=\dfrac{1}{a-b} ln \vert \dfrac{x+b}{x+a} \vert + C, (a \neq b)\)

\(\displaystyle \int \dfrac{xdx}{(x+a)(x+b)}=\dfrac{1}{a-b} (aln|x+a| -bln|x+b|) +C, (a \neq b)\)

\(\displaystyle \int \dfrac{dx}{x^2+a^2}=\dfrac{1}{a} arctan \dfrac{x}{a}+ C, (a \neq b)\)

\(\displaystyle \int \dfrac{xdx}{x^2-a^2}=\dfrac{1}{2} ln|x^2-a^2|+ C\)

\(\displaystyle \int \dfrac{xdx}{x^2+a^2}=\dfrac{1}{2} ln|x^2+a^2|+ C\)

\(\displaystyle \int \dfrac{dx}{(x^2+a^2)^2}=\dfrac{1}{2a^2} \dfrac{x}{x^2+a^2}+\dfrac{1}{2a^3}arctan \dfrac{x}{a}+ C\)

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

\(\displaystyle \int \dfrac{dx}{(x^2+a^2)(x+b)}=\dfrac{1}{a^2+b^2}(ln \dfrac{|x+b|}{\sqrt {x^2+a^2}}+\dfrac{b}{a}arctan \dfrac{x}{a})+ C\)

\(\displaystyle \int \dfrac{xdx}{(x^2+a^2)(x+b)}=\dfrac{1}{a^2+b^2}(arctan \dfrac{x}{a}-bln \dfrac{|x+b|}{\sqrt {x^2+a^2}})+ C\)

\(\)