Search results:
61.
$\int \sin mx \sin nx dx = -\dfrac{\sin(m+n)x}{2(m+n)}+\dfrac{\sin(m-n)x}{2(m-n)} + C, m^2 \ne n^2$
62.
$\int \cos mx \cos nx dx = \dfrac{\sin(m+n)x}{2(m+n)}+\dfrac{\sin(m-n)x}{2(m-n)} + C, m^2 \ne n^2$
65.
Integral of arcsin
$\int \arcsin x dx = x\arcsin x + \sqrt{1-x^2}+C$
66.
$\int \sin mx \cos nx dx = -\dfrac{\cos(m+n)x}{2(m+n)}-\dfrac{\cos(m-n)x}{2(m-n)} + C, m^2 \ne n^2$
67.
Integral of arccos
$\int \arccos x dx = x\arccos x-\sqrt{1-x^2}+C$
68.
Integral of arctan
$\int \arctan x dx = x\arctan x - \dfrac{1}{2}\ln\left(x^2+1\right)+C$
69.
$\int \sqrt{ax+b}dx=\dfrac{2}{3a}\left(ax+b\right)^{3/2}+C$
70.
$\int x\sqrt{ax+b}dx=\dfrac{2(3ax-2b)}{15a^2}(ax+b)^{3/2}+C$
71.
$\int \dfrac{dx}{(x+c)\sqrt{ax+b}}=\dfrac{1}{\sqrt{b-ac}} \ln\left|\dfrac{\sqrt{ax+b}-\sqrt{b-ac}}{\sqrt{ax+b}+\sqrt{b-ac}}\right|+C, b-ac>0$
72.
$\int \dfrac{dx}{(x+c)\sqrt{ax+b}}=\dfrac{1}{\sqrt{ac-b}}\arctan\sqrt{\dfrac{ax+b}{ac-b}}+C, b-ac<0$
73.
$\int x^2\sqrt{a+bx}dx=\dfrac{2\left(8a^2-12abx+15b^2x^2\right)}{105b^3}\sqrt{(a+bx)^3}+C$
74.
$\int \dfrac{x^2}{\sqrt{a+bx}} = \dfrac{2\left(8a^2-4abx+3b^2x^2\right)}{15b^3}\sqrt{a+bx}+C$