anonymous
  • anonymous
How do i find the integral(or antiderivative) of (3-x)(x^2-6x)^5
Mathematics
katieb
  • katieb
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myininaya
  • myininaya
let u=the inside of nastier part.
myininaya
  • myininaya
Hello?
anonymous
  • anonymous
What do you mean?

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anonymous
  • anonymous
u=x^2-6x du=2x-6=2(x-3)
myininaya
  • myininaya
du=-2(3-x) dx -du/2=(3-x)dx
anonymous
  • anonymous
What do I do with the 3-x though?
anonymous
  • anonymous
replace (3-x)dx with -1/2 du
anonymous
  • anonymous
Why do I replace it with -1/2 du?
anonymous
  • anonymous
you want to convert the integral from integral(f(x)dx) to integral(f(u)du) if u=x^2-6x, then u'(x)=du/dx=2(x-3). thus du=dx u'(x)=2(x-3)dx thus -1/2*du=(3-x)dx the original integral is integrate( (3-x)(x^2-6x)^5 dx) =integrate( u^5 (3-x)dx) =integrate ( u^5*(-1/2) du) after integrating, convert back to x using the fact that u=x^2-6x
anonymous
  • anonymous
OH! okay I understand now. Thank you!!

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