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emz13
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How do i find the integral(or antiderivative) of (3x)(x^26x)^5
 one year ago
 one year ago
emz13 Group Title
How do i find the integral(or antiderivative) of (3x)(x^26x)^5
 one year ago
 one year ago

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myininaya Group TitleBest ResponseYou've already chosen the best response.2
let u=the inside of nastier part.
 one year ago

emz13 Group TitleBest ResponseYou've already chosen the best response.0
What do you mean?
 one year ago

eashy Group TitleBest ResponseYou've already chosen the best response.1
u=x^26x du=2x6=2(x3)
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
du=2(3x) dx du/2=(3x)dx
 one year ago

emz13 Group TitleBest ResponseYou've already chosen the best response.0
What do I do with the 3x though?
 one year ago

eashy Group TitleBest ResponseYou've already chosen the best response.1
replace (3x)dx with 1/2 du
 one year ago

emz13 Group TitleBest ResponseYou've already chosen the best response.0
Why do I replace it with 1/2 du?
 one year ago

eashy Group TitleBest ResponseYou've already chosen the best response.1
you 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
 one year ago

emz13 Group TitleBest ResponseYou've already chosen the best response.0
OH! okay I understand now. Thank you!!
 one year ago
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