Evaluating Indefinite Integrals

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Evaluating Indefinite Integrals

Mathematics
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\[\int\limits 2(2x+4)^5dx\] u=2x+4
du=2dx \[\int\limits_{}^{}u^{5}du\]
He's doing well, let him continue. :P

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i got that far lol im stuck with the rest... I know the answer is 1/6(2x+4)^6+c
Okay, so you've got that u = 2x+4. du = 2 * dx, right? Now, put it in terms of dx : dx = du/2.
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.
im not sure if i am supposed to distribute the first "2" or put it in front of the integral
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?
yep... i have \[\int\limits u^5 du \]
There you go. :) Integrate now, and when you're finished, all you have to do is sub 2x+4 back inside for u.
thats where i am having trouble lol i HATE integration... is it u^6/6 +c?
Yep, that's it.
wonderful! i got it now... plug 2x+4 in for x and solve! thank you so much!
Power rule for integration: \[\int\limits \ \ x^n \ dx = \frac{x^{n+1}}{n+1}+c\]
i wish this site had a friends feature lol youd be a lifesaver... literally (not like me)
Lol, no problem.

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