1. ## Indefinite Integral help

I have this problem for homework:

Evaluate the indefinite integral

I don't know how to decide which numbers to pick as the 'u'. Is there a rule to follow, or do you just pick any one at random?

Thank you

2. Originally Posted by JohnJames
I have this problem for homework:

Evaluate the indefinite integral

I don't know how to decide which numbers to pick as the 'u'. Is there a rule to follow, or do you just pick any one at random?

Thank you

$\displaystyle \frac{1}{8} \int \frac{\cos{x}}{\sin{x}+6} \, dx$

$u = \sin{x} + 6$

$du = \cos{x} \, dx$

substitute, integrate, then back substitute ...

$\displaystyle \frac{1}{8} \int \frac{du}{u}$

$\displaystyle \frac{1}{8} \ln{u} + C$

$\displaystyle \frac{1}{8} \ln(\sin{x}+6) + C$

3. Thanks again for your help Skeeter, sorry for the late response.

How did you get:

I don't understand that part of it.

4. you should already know the following general antiderivative ...

$\displaystyle \int \frac{dx}{x} = \ln|x| + C$

Pauls Online Notes : Calculus I - Computing Indefinite Integrals

5. Thanks so much Skeeter, you been a real big help man.