Search results:
281.
$\int \dfrac{xdx}{\sqrt{ax+b}}=\dfrac{2(ax-2b)}{3a^2}\sqrt{ax+b}+C$
282.
$\int \sqrt{\dfrac{ax+b}{cx+d}}dx=\dfrac{1}{c}\sqrt{(ax+b)(cx+d)}-\dfrac{ad-bc}{c\sqrt{ac}}\ln\left|\sqrt{a(cx+d)}+\sqrt{c(ax+b)}\right|+C, a>0$
283.
$\int \sqrt{\dfrac{ax+b}{cx+d}}dx=\dfrac{1}{c}\sqrt{(ax+b)(cx+d)}-\dfrac{ad-bc}{c\sqrt{ac}}\arctan\sqrt\frac{a(cx+d)}{c(ax+b)}+C, a<0,c>0$
291.
$\int \cos^3x dx = \dfrac{1}{12}\sin 3x +\dfrac{3}{4}\sin x + C$
293.
$\int \dfrac{dx}{\cos x}=\ln\left|\tan\left(\frac{x}{2}+\frac{\pi}{4}\right)\right|+C$
296.
$\int \dfrac{dx}{\sin^3x} =-\dfrac{\cos x}{2 \sin^2x}+\dfrac{1}{2}\ln\left|\tan\dfrac{x}{2}\right|+C$
297.
$\int \dfrac{dx}{\cos^3x}=\dfrac{\sin x}{2 \cos^2x}+\dfrac{1}{2}\ln\left|\tan\left(\frac{x}{2}+\frac{\pi}{4}\right)\right|+C$