Search results:
241.
The chain rule - general formula for composite functions
$\left(f\left(g(x)\right)\right)'=f'(g(x))\cdot g'(x)$
252.
$\int \left(ax+b\right)^n \,dx=\dfrac{\left(ax+b\right)^{n+1}}{a(n+1)}+C, n \ne 1$
255.
$\int \dfrac{ax+b}{cx+d}dx=\dfrac{a}{c}x+\dfrac{bc-ad}{c^2} \ln|cx+d|+C$
256.
$\int \dfrac{dx}{(x+a)(x+b)} dx=\dfrac{1}{a-b}+\ln\left| \dfrac{x+b}{x+a}\right|+C, a\ne b$
257.
$\int \dfrac{x}{a+bx}dx=\dfrac{1}{b^2}\left(a+bx-a\ln|a+bx|\right) + C$
258.
$\int \dfrac{x^2 dx}{a+bx}=\dfrac{1}{b^3}\left[ \dfrac{1}{2} (a+bx)^2 - 2a(a+bx)+a^2\ln|a+bx|\right]+C$
259.
$\int \dfrac{dx}{x(a+bx)}dx=\dfrac{1}{a} \ln \left| \dfrac{a+bx}{x} \right| + C$
260.
$\int \dfrac{dx}{x^2(a+bx)}dx=-\dfrac{1}{ax}+\dfrac{b}{a^2} \ln\left|\dfrac{a+bx}{x}\right|+C$