求积分!∫sinx/(a+bcosx)dx

1.当b=0时,
∫sinx/(a+bcosx)dx=1/a∫sinxdx
=-cosx/a+C (C是积分常数)
当b≠0时,
∫sinx/(a+bcosx)dx=-1/b∫d(a+bcosx)/(a+bcosx)
=-ln│a+bcosx│/b+C (C是积分常数)
2.当b=0时,
∫xcos(a+bx^2)dx=cosa∫xdx
=x²cosa/2+C (C是积分常数)
当b≠0时,
∫xcos(a+bx^2)dx=1/(2b)∫cos(a+bx^2)d(a+bx^2)
=sin(a+bx^2)/(2b)+C (C是积分常数)
3.∫[x^4sin(4x^5)]dx=1/20∫sin(4x^5)d(4x^5)
=-cos(4x^5)/20+C (C是积分常数)
4. ∫dx/[√x(√x-1)]=2∫d(√x-1)/(√x-1)
=2ln│√x-1│+C (C是积分常数).