Question

∫x*√(1-x^2) dx

Answer 1

原式=(1/2)∫√(1-x²)dx²=(-1/2)∫√(1-x²)d(1-x²)=(-1/2)(2/3)(1-x²)^(3/2)+C=(-1/3)*(1-x²)^(3/2) +C

Answer 2

x=sint
cost=√(1-x^2)=(1-x^2)^(1/2)
dx=cost*dt
∫x*√(1-x^2) dx=
∫(sint)*(cost) cost*dt=
∫(cost)^2*(sint*dt)=-1/3*(cost)^3+C=-1/3*(1-x^2)^(3/2)+C