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anonymous
 3 years ago
How do i find the integral(or antiderivative) of (3x)(x^26x)^5
anonymous
 3 years ago
How do i find the integral(or antiderivative) of (3x)(x^26x)^5

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myininaya
 3 years ago
Best ResponseYou've already chosen the best response.2let u=the inside of nastier part.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0u=x^26x du=2x6=2(x3)

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.2du=2(3x) dx du/2=(3x)dx

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0What do I do with the 3x though?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0replace (3x)dx with 1/2 du

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Why do I replace it with 1/2 du?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you want to convert the integral from integral(f(x)dx) to integral(f(u)du) if u=x^26x, then u'(x)=du/dx=2(x3). thus du=dx u'(x)=2(x3)dx thus 1/2*du=(3x)dx the original integral is integrate( (3x)(x^26x)^5 dx) =integrate( u^5 (3x)dx) =integrate ( u^5*(1/2) du) after integrating, convert back to x using the fact that u=x^26x

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0OH! okay I understand now. Thank you!!
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