Can anybody help me solving integral problems? help me solve the following with clear solutions

1. integral of cos 4x sin^(4) x dx
2. integral of cos^(3) x sin 4x dx
3. integral of xe^(2x) cos x dx
4. integral of (x^3 + 2x + sin x) e^(3x) dx


thank you for clear solutions

The solutions are as follows --

1) (3/32)*sin(4*x)+(1/128)*sin(8*x) + (1/16)*x-(1/8)*sin(2*x)-(1/24)*sin(6*x) + C

2) (1/392)*sin(7*x)-(1/56)*x*cos(7*x) + (1/8)*sin(x)-(1/8)*x*cos(x) + (3/200)*sin(5*x)-(3/40)*x*cos(5*x) +(1/24)*sin(3*x)-(1/8)*x*cos(3*x) + C

3) ((2/5)*x-3/25)* exp(2*x)*cos(x) - (-(1/5)*x+4/25)*exp(2*x) *sin(x) + C

4) (1/3)*(exp(x))^3*x^3-(1/3)* x^2*(exp(x))^3 + (8/9)*(exp(x))^3*x-(8/27)*(exp(x))^3 -(1/10) * exp(3*x)*cos(x)+(3/10)*exp(3*x)*sin(x) + C

I can't show work here because its too much. But you can always send me a mail if needed