Question

Integration:

Answer 1

\[\LARGE \int x~(2x+5)^8~dx\]

Answer 2

We can use integration using substitution for this one.

Answer 3

assume
2x+5=u

Answer 4

Right

Answer 5

Then, du/dx=2
So, du=2dx

Answer 6

\[\int\limits_{}^{}x(2x+5)^8dx=\int\limits_{}^{}xu^8*1/2*du\]

Answer 7

Now, from the substituion u=2x+5, we get x=(u-5)/2

Answer 8

\[\int\limits_{}^{}(\frac{ 1 }{ 2 })(\frac{ u-5 }{ 2 })u^8du=\int\limits_{}^{}\frac{ u^9-5u^8 }{ 4 }du\]

Answer 9

Can you take it from here?
@Luigi0210

Answer 10

Yes, I got the rest, thanks for the explanation as well :)

Answer 11

Yep!
Just make sure to leave your answer in terms of x, not u

Answer 12

Math @-@