Indefinite Integral help

**JohnJames** · July 11th 2010, 01:09 PM

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

**skeeter** · July 11th 2010, 01:26 PM

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 ...

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

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

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

**JohnJames** · July 11th 2010, 04:30 PM

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

How did you get:

I don't understand that part of it.

**skeeter** · July 11th 2010, 05:35 PM

you should already know the following general antiderivative ...

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

link ...

Pauls Online Notes : Calculus I - Computing Indefinite Integrals

**JohnJames** · July 11th 2010, 06:02 PM

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

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