1,∫[（7cosx-sinx)/(5cosx+2sinx)]dx2,∫([x^3)/(9+x^2)]dx3,∫e^(-ax)dx上限+无穷；下限04,∫1sinx1dx上限2pai；下限0;;;;11为绝对值5,d/dx{∫cos(pait^2)dt}

Question

1,∫[（7cosx-sinx)/(5cosx+2sinx)]dx
2,∫([x^3)/(9+x^2)]dx
3,∫e^(-ax) dx 上限+无穷；下限0
4,∫1sinx1dx 上限2pai；下限0 ;;;;1 1 为绝对值
5,d/dx {∫cos(pait^2)dt}

Answer 1

1,乘开 35cos^2x-9/2sin2x-5sin^2=40∫cos^2xdx-9/4∫sin2xd2x-∫5dx=40∫1/2(cos2x+1)dx+9/4cos2x-5x=10∫cos2xd2x+9/4cos2x+15x=10sin2x+9/4cos2x+15x+C.2,=1/2∫x^2/(9+x^2)dx^2=1/2∫t/(t+9)dt=1/2∫1-9/(t+9)dt...