# Thread: Help identifying substitution value for integral

1. ## Help identifying substitution value for integral

The question:
Use a substitution to evaluate $\displaystyle \int x(5x -1)^{19} dx$

My attempt:
Normally I'd check to see if value within the brackets is an anti-derivative of the element outside (chain rule). In this case, it isn't. I'm uncertain as to how I should go about finding a substitution. Any ideas? Thanks.

2. Originally Posted by Glitch
The question:
Use a substitution to evaluate $\displaystyle \int x(5x -1)^{19} dx$

My attempt:
Normally I'd check to see if value within the brackets is an anti-derivative of the element outside (chain rule). In this case, it isn't. I'm uncertain as to how I should go about finding a substitution. Any ideas? Thanks.
$\displaystyle \displaystyle\ u=5x-1\Rightarrow\ \frac{du}{dx}=5\Rightarrow\ \frac{du}{5}=dx$

$\displaystyle \displaystyle\frac{u+1}{5}=x$

$\displaystyle \displaystyle\int{x(5x-1)^{19}dx=\int{\frac{u+1}{5}u^{19}\frac{du}{5}=\fr ac{1}{25}\int{(u+1)u^{19}}du=\frac{1}{25}\int{\lef t(u^{20}+u^{19}\right)}du$

3. I really need to get better at spotting these tricks! Thanks!

4. response edited.

5. Hehe, thanks. I went to do it myself and noticed you made an error. :P