Question

求不定积分打勾的题谢谢各位大佬

Answer 1

(30)
∫e^(-3x) sin(4x) dx
=-(1/3)∫ sin(4x) de^(-3x)
=-(1/3)sin(4x).e^(-3x)+(4/3)∫ cos(4x) .e^(-3x) dx
=-(1/3)sin(4x).e^(-3x) -(4/9)∫ cos(4x) de^(-3x)
=-(1/3)sin(4x).e^(-3x) -(4/9)cos(4x).e^(-3x) -(16/9)∫ sin(4x).e^(-3x) dx
(25/9)∫e^(-3x) sin(4x) dx=-(1/3)sin(4x).e^(-3x) -(4/9)cos(4x).e^(-3x)
∫e^(-3x) sin(4x) dx
=(9/25)[-(1/3)sin(4x).e^(-3x) -(4/9)cos(4x).e^(-3x)] +C
(31)
∫lnx/[x√x] dx
=-2∫lnx dx^(-1/2)
=-2lnx/√x + 2∫ x^(-3/2) dx
=-2lnx/√x - 4/√x +C
(38)
∫x^2. sin[x^(3/2)] dx
=-(2/3)∫x^(3/2) dcos[x^(3/2)]
=-(2/3) x^(3/2).cos[x^(3/2)] +∫x^(1/2) cos[x^(3/2)] dx
=-(2/3) x^(3/2).cos[x^(3/2)] +(2/3)∫dsin[x^(3/2)]
=-(2/3) x^(3/2).cos[x^(3/2)] +(2/3)sin[x^(3/2)] + C