More complex indefinite integrals by substitution

**fattydq** · February 13th 2009, 02:06 PM

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.

**fattydq** · February 13th 2009, 02:28 PM

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

**HallsofIvy** · February 13th 2009, 02:37 PM

Originally Posted by fattydq

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

(7) is $\int (x+ 34)\sqrt{68x+ x^2}dx$
The only reasonable substitution is $u= 68x+ x^2$ . That just happens to work nicely because du= (68+ 2x)dx= 2(34+ x)dx!

**javax** · February 13th 2009, 02:40 PM

sub. $68x+x^2=t \Rightarrow (2x+68)dx = dt$ which you can simplify to $(x+34)dx=\frac{dt}{2}$ now the integral will be $\frac{1}{2}\int{t^{\frac{1}{2}}dt} = ...$

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