Search results:
261.
$\int \dfrac{xdx}{\left(a+bx\right)^2}=\dfrac{1}{b^2} \left( \ln \left|a+bx\right|+\dfrac{a}{a+bx}\right) + C$
262.
$\int \dfrac{x^2}{\left(a+bx\right)^2}=\dfrac{1}{b^3} \left(a+bx-2a\ln|a+bx|-\dfrac{a^2}{a+bx}\right)+C$
263.
$\int \dfrac{dx}{x(a+bx)^2}=\dfrac{1}{a(a+bx)}+\dfrac{1}{a^2}\ln\left|\dfrac{a+bx}{x}\right|+C$
264.
$\int \dfrac{dx}{x^2-1}=\dfrac{1}{2}\ln\left|\dfrac{x-1}{x+1}\right|+C$
265.
$\int \dfrac{dx}{1-x^2}=\dfrac{1}{2}\ln\left|\dfrac{1+x}{1-x}\right|+C$
266.
$\int \dfrac{dx}{a^2-x^2}=\dfrac{1}{2a}\ln\left|\dfrac{a+x}{a-x}\right|+C$
267.
$\int \dfrac{dx}{x^2-a^2}=\dfrac{1}{2a}\ln\left|\dfrac{x-a}{x+a}\right|+C$
269.
$\int \dfrac{dx}{a^2+x^2}=\dfrac{1}{a}\tan^{-1}\dfrac{x}{a}+C$
270.
$\int \dfrac{dx}{a+bx^2}=\dfrac{1}{\sqrt{ab}}\arctan \left(x\sqrt{\dfrac{a}{b}}\right)+C, ab>0$
271.
$\int \dfrac{xdx}{a+bx^2}=\dfrac{1}{2b}\ln\left|x^2+\frac{a}{b}\right|+C$
272.
$\int \dfrac{dx}{x\left(a+bx^2\right)}=\dfrac{1}{2a}\ln\left|\dfrac{x^2}{a+bx^2}\right|+C$
273.
$\int \frac{dx}{a^2-b^2x^2}=\dfrac{1}{2ab}\ln\left|\dfrac{a+bx}{a-bx}\right|+C$
274.
$\int \dfrac{dx}{ax^2+bx+c}=\dfrac{1}{\sqrt{b^2-4ac}}\ln\left| \dfrac{2ax+b-\sqrt{b^2-4ac}}{2ax+b+\sqrt{b^2-4ac}} \right|+C, b^2-4ac>0$
275.
$\int \dfrac{dx}{ax^2+bx+c}=\dfrac{2}{\sqrt{4ac-b^2}} \arctan \dfrac{2ax+b}{\sqrt{4ac-b^2}}+C$
278.
Derivative of inverse coth
$\dfrac{d}{dx}\, \left( \coth^{-1} x\right) = \dfrac{1}{1-x^2}$
280.
$\int \dfrac{dx}{\sqrt{a+bx}}=\dfrac{2}{a}\sqrt{ax+b}+C$