Search results:
22.
$\int \dfrac{dx}{a^2+x^2}=\dfrac{1}{a}\tan^{-1}\dfrac{x}{a}+C$
23.
$\int \dfrac{dx}{a+bx^2}=\dfrac{1}{\sqrt{ab}}\arctan \left(x\sqrt{\dfrac{a}{b}}\right)+C, ab>0$
24.
$\int \dfrac{xdx}{a+bx^2}=\dfrac{1}{2b}\ln\left|x^2+\frac{a}{b}\right|+C$
25.
$\int \dfrac{dx}{x\left(a+bx^2\right)}=\dfrac{1}{2a}\ln\left|\dfrac{x^2}{a+bx^2}\right|+C$
26.
$\int \frac{dx}{a^2-b^2x^2}=\dfrac{1}{2ab}\ln\left|\dfrac{a+bx}{a-bx}\right|+C$
27.
$\int \dfrac{dx}{ax^2+bx+c}=\dfrac{1}{\sqrt{b^2-4ac}}\ln\left| \dfrac{2ax+b-\sqrt{b^2-4ac}}{2ax+b+\sqrt{b^2-4ac}} \right|+C, b^2-4ac>0$
28.
$\int \dfrac{dx}{ax^2+bx+c}=\dfrac{2}{\sqrt{4ac-b^2}} \arctan \dfrac{2ax+b}{\sqrt{4ac-b^2}}+C$
29.
$\int \dfrac{dx}{\sqrt{a+bx}}=\dfrac{2}{a}\sqrt{ax+b}+C$
30.
$\int \dfrac{xdx}{\sqrt{ax+b}}=\dfrac{2(ax-2b)}{3a^2}\sqrt{ax+b}+C$
31.
$\int \sqrt{\dfrac{ax+b}{cx+d}}dx=\dfrac{1}{c}\sqrt{(ax+b)(cx+d)}-\dfrac{ad-bc}{c\sqrt{ac}}\ln\left|\sqrt{a(cx+d)}+\sqrt{c(ax+b)}\right|+C, a>0$
32.
$\int \sqrt{\dfrac{ax+b}{cx+d}}dx=\dfrac{1}{c}\sqrt{(ax+b)(cx+d)}-\dfrac{ad-bc}{c\sqrt{ac}}\arctan\sqrt\frac{a(cx+d)}{c(ax+b)}+C, a<0,c>0$
40.
$\int \cos^3x dx = \dfrac{1}{12}\sin 3x +\dfrac{3}{4}\sin x + C$