x∧2/根号(1-x∧2)的积分
网友回答
设 x = sint,则 dx = cost*dt
∫x^2/√(1-x^2) *dx
=∫(sint)^2 *(cost)*dt/cost
=∫(sint)^2 *dt
=1/2*∫2(sint)^2 *dt
=1/2*∫(1-cos2t)*dt
=1/2*∫dt - 1/2*∫cos2t*dt
=1/2*t - 1/4*sin2t + C
=1/2*arcsinx - 1/2*sint*cost + C
=1/2*arcsinx - 1/2*x*√(1-x^2) + C