Integration Help | Homework Equations & Solutions

[Unintended]

Homework Statement

I have three separate equations that I would really appreciate your help on.

Homework Equations

The first is (lnx)^2 dx
The Second is e^x sin(3x) dx
The third is a definitive integral between pi and zero, sin^3(x) dx

The Attempt at a Solution

I am unsure as to how to go about the second two, but would the first go something like
lnx=u
x=e^y
dx=e^u du

Integration comes quite badly to me. I would appreciate a step by step to see what I am actually meant to be doing.

 

[Cyosis]

1)

I am unsure as to how to go about the second two, but would the first go something like
lnx=u
x=e^y
dx=e^u du

That works, how did you continue from here?

2) Works very similar to the second part of 1) try it out and show us where you get stuck (integration by parts).

3)Use $\sin^2x+\cos^2x=1$.

You will need to show your work, because we don't hand out answers.