Integration by Parts 5x ln(4x)dx

[sashab]

Homework Statement

Use integration by parts to evaluate the integral.
∫5x ln(4x)dx

Homework Equations

∫udv = uv - ∫vdu

The Attempt at a Solution

So here's my solution:

But the computer is telling me I'm wrong :( We haven't learned how to integrate lnx yet, so the only choice I have is to make u = ln(4x) (even our textbook does this). Any help would be really appreciated! Thanks :)

 

[SammyS]

Homework Statement

Use integration by parts to evaluate the integral.
∫5x ln(4x)dx

Homework Equations

∫udv = uv - ∫vdu

The Attempt at a Solution

So here's my solution:

But the computer is telling me I'm wrong :( We haven't learned how to integrate lnx yet, so the only choice I have is to make u = ln(4x) (even our textbook does this). Any help would be really appreciated! Thanks :)

What is the derivative of ln(4x) ?

 

[sashab]

What is the derivative of ln(4x) ?

Oh whoops! I can't believe I didn't notice such an obvious mistake. Thanks, I got the right answer now. :)

 

[HallsofIvy]

By the chain rule, the derivative of ln(4x) is (1/4x) times the derivative of 4x so (1/4x)(4)= 1/x.

Even simpler: ln(4x)= ln(x)+ ln(4) so its derivative is 1/x.