anonymous
  • anonymous
Find the anti derivative of (x)^(1/2)(6 + 5x) I'm completely lost with these questions can some one show me the step by step method? An explanation would also be apprciated but I dont expect one
Mathematics
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Joachim
  • Joachim
http://www.khanacademy.org/math/calculus/v/the-indefinite-integral-or-anti-derivative
anonymous
  • anonymous
Yeah that video isn't helpful I know how to take the antiderivative I just dont know how to take the anti derivative of products
anonymous
  • anonymous
Set u = (x)^(1/2) dx/2(x)^(1/2) = dt What do I do next?

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ash2326
  • ash2326
We have \[\int x^{\frac{1}{2}}(6+5x)dx\] Just mulitply \(x^{\frac{1}{2}}\) to all the terms We get \[\large \int (6x^{\frac{1}{2}}+5x^{\frac{3}{2}})dx\] We know the integral of \[\int x^n dx= \frac{x^{n+1}}{n} when\ n\ne -1\] so here we'll use this We get \[\large \frac{6x^{(\frac{1}{2}+1)}}{\frac{1}{2}+1}+\frac{5x^{\frac{3}{2}+1}}{\frac{3}{2}+1}+C\] We get finally \[\large \int x^{\frac{1}{2}}(6+5x)dx= \frac{6x^{\frac{3}{2}}}{\frac{3}{2}}+\frac{5x^{\frac{5}{2}}}{\frac{5}{2}}+C\]

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