Two integrals that I don't know how to solve

[vsportsguy]

Homework Statement

There are two integrals that I don't know how to solve. I'm fairly certain the preceding work that led me to these integrals is correct.

Homework Equations

1. ∫sin (x) / (csc (x) + cot (x))
2. ∫x^(2) / (1 - x)

The Attempt at a Solution

U substitution didn't work for either integral. Is integration by parts the correct way to go?

Thank You

 

[Mark44]

Homework Statement

There are two integrals that I don't know how to solve. I'm fairly certain the preceding work that led me to these integrals is correct.

Homework Equations

1. ∫sin (x) / (csc (x) + cot (x))
2. ∫x^(2) / (1 - x)

The Attempt at a Solution

U substitution didn't work for either integral. Is integration by parts the correct way to go?

Thank You

Integration by parts is NOT the way to go!

Also, don't forget the "dx". As the integrals get more complicated, omitting this symbol will definitely cause problems.

For the first integral, use the basic trig identities to get everything in terms of sine and cosine.

For the second, one approach is to use polynomial long division to divide x² by 1 - x. Or, you can write x²/(1 - x) as (x² - 1 + 1)/(1 - x), and split into two integrals.