Question

I'm trying to integrate dx/(5x+9)^2 so I've made u=5x+9, and du= 5dx. now I'm integrating (du/5)/u^2. How do I do that, or have I chosen the wrong u?

Answer 1

use the power rule backwards

Answer 2

\[\int u^n du =\frac{u^{n+1}}{n+1}\]

Answer 3

So I'll want to transform it into 1/5u^2 du and then does the 1/5 coefficient stay with my u^2 when I inverse power rule it, like, (1/5u^3)/3?

Answer 4

\[\large \int\limits \frac{dx}{(5x+9)^2}\] let u = 5x+9 du = 5dx du/5 = dx \[\large \int\limits \frac{du/5}{u^2} \implies \int\limits \frac{du}{5u^2}\]\[\large \large \frac{1}{5} \int\limits \frac{du}{u^2}\] can you take it from there?

Answer 5

I've got it now, thanks guys!