# More complex indefinite integrals by substitution

• Feb 13th 2009, 02:06 PM
fattydq
More complex indefinite integrals by substitution
I've attached a picture with two more problems I'm working on. For the first I have no idea what to use as u because it seems differentiating any term won't give you part of another term in the problem.

As for the second one, the fact that there's a dt in the numerator is throwing me off and I don't know what to do in problems like this.
• Feb 13th 2009, 02:28 PM
fattydq
Ok I figured out #8, anyone want to help me out with the other?
• Feb 13th 2009, 02:37 PM
HallsofIvy
Quote:

Originally Posted by fattydq
Ok I figured out #8, anyone want to help me out with the other?

(7) is $\displaystyle \int (x+ 34)\sqrt{68x+ x^2}dx$
The only reasonable substitution is $\displaystyle u= 68x+ x^2$. That just happens to work nicely because du= (68+ 2x)dx= 2(34+ x)dx!
• Feb 13th 2009, 02:40 PM
javax
sub. $\displaystyle 68x+x^2=t \Rightarrow (2x+68)dx = dt$which you can simplify to$\displaystyle (x+34)dx=\frac{dt}{2}$now the integral will be $\displaystyle \frac{1}{2}\int{t^{\frac{1}{2}}dt} = ...$