anonymous
  • anonymous
find the following indefinite integral using u-substitution to solve... HELP
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[\int\limits_{}^{}6x \sqrt{x^2-25}dx\]
anonymous
  • anonymous
I know I let u=x^2-25 which makes du=2xdx
anonymous
  • anonymous
i am stuck at a particular step.. i will show you what i have so far

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mathmate
  • mathmate
hint: try u=sqrt(x^2-25) or try differentiating sqrt(x^2-25) and see what you get.
dumbcow
  • dumbcow
ok then dx = du/2x \[\int\limits_{}^{}\frac{6x \sqrt{u}}{2x} du =3 \int\limits_{}^{}\sqrt{u} du\]
anonymous
  • anonymous
\[\int\limits_{}^{}\sqrt{x^2-25}\times6xdx = 3\int\limits_{}^{}\sqrt{x^2-25}\times2xdx = 3\int\limits_{}^{}\sqrt{u}du\]
anonymous
  • anonymous
i'm lost after that
dumbcow
  • dumbcow
\[\sqrt{u} = u^{1/2}\] use the power rule
dumbcow
  • dumbcow
\[\large \int\limits_{}^{}x^{n} = \frac{x^{n+1}}{n+1}\]
anonymous
  • anonymous
yeah so i would fill fill in x^2 -25 now for that step or no?
dumbcow
  • dumbcow
no leave it in terms of u until you have finished integrating, then the last step will be to substitute the x^2 -25 back in for u
anonymous
  • anonymous
ok so i got 2u^(3/2)+c ... is that correct?
dumbcow
  • dumbcow
yep
anonymous
  • anonymous
ok so then substitute in now? giving me.. 2(x^2-25)^(3/2) + c ..?
dumbcow
  • dumbcow
yes you could also write it as ...2sqrt(x^2-25)(x^2 -25) + c
anonymous
  • anonymous
ok so then my final answer is \[2x^2-50\sqrt{x^2-25}+c\]..? or just leave it \[2(x^2-25)\sqrt{x^2-25}+c\]?
dumbcow
  • dumbcow
i would just leave it in factored form, but both are correct
anonymous
  • anonymous
thank you so much!

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