(arcsinx)^2的不定积分
问题描述：
(arcsinx)^2的不定积分
答
设 t = arcsinx,则 x = sint,dx = cost*dt.则：
∫(arcsinx)^2 * dx
=∫t^2 * cost * dt
=t^2 * sint - ∫sint * 2t * dt
=t^2 * sint - 2*∫(t*sint)*dt
=t^2 * sint - 2*[ t * (-cost) - ∫(-cost)*dt]
=t^2 * sint - 2*[-t * cost + sint]
=t^2 * sint + 2t * cost - 2 * sint + C
=(arcsinx)^2 * x + 2(arcsinx)*√(1-x^2) - 2x + C