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

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

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

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

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

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

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

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

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