Question

Need help on the next step of this definite integral

Answer 1

\[\int\limits_{1}^{2} 3x/\sqrt{4x+5} dx\]

I used the u-sub of sqrt{4x+5}, u^2=4x+5 got 2udu=4dx and then udu=2dx.

I feel like the next step is right in front of my eyes but I'm just not seeing it

Answer 2

when you sub in for dx, the u will cancel with the sqrt(4x+5) since it is equal to u
replace x with (u^2 -5)/4

\[\rightarrow \frac{3}{8}\int\limits_{1}^{2}(u^{2}-5) du\]

Answer 3

Can I just pull the 3 out from the x like that?

Answer 4

oh sorry i didn't see you responded

yes you can, anytime it is a constant
\[\int\limits_{?}^{?}n*x dx= n \int\limits_{?}^{?}x dx\]

Answer 5

np, gave me time to try to figure it all out, lol.