Primitive of x by Arcsine of x over a

Theorem

 * $\displaystyle \int x \arcsin \frac x a \ \mathrm d x = \left({\frac {x^2} 2 - \frac {a^2} 4}\right) \arcsin \frac x a + \frac {x \sqrt {a^2 - x^2} } 4 + C$

Also see

 * Primitive of $x \arccos \dfrac x a$


 * Primitive of $x \arctan \dfrac x a$


 * Primitive of $x \operatorname{arccot} \dfrac x a$


 * Primitive of $x \operatorname{arcsec} \dfrac x a$


 * Primitive of $x \operatorname{arccsc} \dfrac x a$