1) You can use u-substitution, so no.
2) This can be solved using integration by parts. Let u = x and v ' = e3x. Using the DI method is the simplest way.
+ x e3x
+ 0 (e3x)/9
Adding the diagonal multiplications:
Integral = x(e3x)/3 - (e3x)/9 + C = (3x-1)e3x/9 + C
3) You can use trig identities to simplify and solve this one
4) You can use the trig reduction formula to simplify and solve this one. However, the reduction formula is derived from integration by parts, i.e. u=cos(x) v ' = cos(x)