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

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

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

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

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

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

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

emz13 Group TitleBest ResponseYou've already chosen the best response.0
Why do I replace it with 1/2 du?
 10 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
 10 months ago

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