求不定积分[x-(arctanx)^(3/2)]/(1+x^2)
问题描述:
求不定积分[x-(arctanx)^(3/2)]/(1+x^2)
答
令t=arctanx,所以tant=x,[x-(arctanx)^(3/2)]/(1+x^2)=[tant-t^(3/2)]dt= -ln|cost|-2/5t^(5/2)+c又因为t=arctanx tant=x 所以|cost|=【1/(x^2+1)】^(1/2)所以原式=(1/2)ln(x^2+1)-(2/5)(arcta...