《积分公式大全》

$$ 113.\,\int\!\! \arcsin \frac{x}{a} dx = x \arcsin \frac{x}{a}+ \sqrt{a^2-x^2} +C $$

$$ 114.\,\int\!\! x\arcsin \frac{x}{a} dx = \Big ( \frac{x^2}{2}-\frac{a^2}{4}\Big )\arcsin \frac{x}{a} + \frac{x}{4}\sqrt {a^2-x^2} +C $$

$$ 115.\,\int\!\! x^2 \arcsin \frac{x}{a}dx= \frac{x^3}{3} \arcsin \frac{x}{a} + \frac{1}{9}(x^2+2a^2)\sqrt{a^2-x^2}+C $$

$$ 116.\,\int\!\! \arccos \frac{x}{a}dx= x \arccos \frac{x}{a}-\sqrt {a^2-x^2} +C $$

$$ 117.\,\int\!\! x \arccos \frac{x}{a} dx = \Big ( \frac{x^2}{2}-\frac{a^2}{4}\Big) \arccos \frac{x}{4} - \frac{x}{4}\sqrt {a^2 -x^2} +C $$

$$ 118.\,\int\!\! x^2\arccos \frac{x}{a} dx = \frac{x^3}{a} \arccos \frac{x}{a} - \frac{1}{9}(x^2 +2a^2)\sqrt{a^2-x^2}+C $$

$$ 119.\,\int\!\! \arctan \frac{x}{a} dx =x \arctan \frac{x}{a} - \frac{a}{2}\ln(a^2+x^2)+C $$

$$ 120.\,\int\!\! x\arctan \frac{x}{a}dx = \frac{1}{2}(a^2+x^2)\arctan \frac{x}{a}-\frac{a}{2}x+C $$

$$ 121.\,\int\!\! x^2 \arctan \frac{x}{a}dx = \frac{x^3}{3}\arctan \frac{x}{a} - \frac{a}{6}x^2+ \frac{a^3}{6}\ln (a^2+x^2)+C $$