## anonymous 5 years ago Evaluating Indefinite Integrals

1. anonymous

$\int\limits 2(2x+4)^5dx$ u=2x+4

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

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

6. anonymous

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.

7. anonymous

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

8. anonymous

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?

9. anonymous

yep... i have $\int\limits u^5 du$

10. anonymous

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

11. anonymous

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

12. anonymous

Yep, that's it.

13. anonymous

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

14. anonymous

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

15. anonymous

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

16. anonymous

Lol, no problem.