# Indefinite Integral help

• July 11th 2010, 01:09 PM
JohnJames
Indefinite Integral help
I have this problem for homework:

Evaluate the indefinite integral

https://webwork2.uncc.edu/webwork2_f...ccac58f0a1.png

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
• July 11th 2010, 01:26 PM
skeeter
Quote:

Originally Posted by JohnJames
I have this problem for homework:

Evaluate the indefinite integral

https://webwork2.uncc.edu/webwork2_f...ccac58f0a1.png

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 ...

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

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

$\displaystyle \frac{1}{8} \ln(\sin{x}+6) + C$
• July 11th 2010, 04:30 PM
JohnJames
Thanks again for your help Skeeter, sorry for the late response.

How did you get:

http://www.mathhelpforum.com/math-he...bd46367f18.png

I don't understand that part of it.
• July 11th 2010, 05:35 PM
skeeter
you should already know the following general antiderivative ...

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