Can someone lend a hand with these integration problems?

[shadezofemerald]

Please find the integrals of:

1) cosxsin^3x dx

2) sin^2xcos^2x dx

3) sin^3xe^(x/2)  dx

any help is greatly appreciated ^_^

[Collin Li]

Question 1
Use a substitution:

Question 2



Now use to find:



Therefore,

Easy to go from there?

Question 3



This isn't required for the Specialist Maths course.

[shadezofemerald]

thanks coblin for your help ^_^

sorri the third questions was supposed to be: find the integral of sin^3(x/2)

[Collin Li]

Oh okay, in that case:

Question 3



Now, use substitution

[shadezofemerald]

ok, thanks heaps!!