Help identifying substitution value for integral

• Oct 26th 2010, 06:52 AM
Glitch
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.
• Oct 26th 2010, 06:58 AM
Quote:

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.

$\displaystyle \displaystyle\ u=5x-1\Rightarrow\ \frac{du}{dx}=5\Rightarrow\ \frac{du}{5}=dx$

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

$\displaystyle \displaystyle\int{x(5x-1)^{19}dx=\int{\frac{u+1}{5}u^{19}\frac{du}{5}=\fr ac{1}{25}\int{(u+1)u^{19}}du=\frac{1}{25}\int{\lef t(u^{20}+u^{19}\right)}du$
• Oct 26th 2010, 07:00 AM
Glitch
I really need to get better at spotting these tricks! Thanks!
• Oct 26th 2010, 07:14 AM