Question

Evaluating Indefinite Integrals

Answer 1

\[\int\limits 2(2x+4)^5dx\]

u=2x+4

Answer 2

du=2dx
\[\int\limits_{}^{}u^{5}du\]

Answer 3

He's doing well, let him continue. :P

Answer 4

i got that far lol im stuck with the rest... I know the answer is 1/6(2x+4)^6+c

Answer 5

Okay, so you've got that u = 2x+4. du = 2 * dx, right? Now, put it in terms of dx : dx = du/2.

Answer 6

In your original integral, replace all (2x+4) with u, and all dx with du/2. The original 2 in front will cancel out, and you'll be left integrating u^5 du. :) Integrate, and plug the value for u back into it.

Answer 7

im not sure if i am supposed to distribute the first "2" or put it in front of the integral

Answer 8

The two can stay inside or outside of the integral, but it would make life a lot easier to not distribute it through your polynomial. :P Do you understand the substitution?

Answer 9

yep... i have \[\int\limits u^5 du \]

Answer 10

There you go. :) Integrate now, and when you're finished, all you have to do is sub 2x+4 back inside for u.

Answer 11

thats where i am having trouble lol i HATE integration... is it u^6/6 +c?

Answer 12

Yep, that's it.

Answer 13

wonderful! i got it now... plug 2x+4 in for x and solve! thank you so much!

Answer 14

Power rule for integration: \[\int\limits \ \ x^n \ dx = \frac{x^{n+1}}{n+1}+c\]

Answer 15

i wish this site had a friends feature lol youd be a lifesaver... literally (not like me)

Answer 16

Lol, no problem.