Math Is Fun Forum

easilydoctor

Member

Registered: 2007-11-18

Posts: 5

Final Exam Help!

∫[(5x²-3x+2)/√x]dx

∫[(sin5x)/(1+cos5x)²]dx

Can somebody quickly solve these for me please?
Also, is there an actual method in doing these besides intuitive trial and error?

Thanks a ∞!

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Final Exam Help!

∫[(5x²-3x+2)/√x]dx

∫[(sin5x)/(1+cos5x)²]dx

Can somebody quickly solve these for me please?
Also, is there an actual method in doing these besides intuitive trial and error?

Thanks a ∞!

Disclaimer: I have not had much experience with integrals

For the first one, just divide through:

For the second, let u = cos(5x), then du = -5sin(5x)dx. We get

Last edited by Identity (2007-12-17 23:35:40)

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: Final Exam Help!

There's a slightly easier substitution that you can use for the second integral.  Let u = cos(5x) + 1.  Then you still have du = -5sin(5x)dx, giving you the integral

---

Wrap it in bacon