anonymous
  • anonymous
Evaluate the following indefinite integrals.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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amoodarya
  • amoodarya
1 Attachment
anonymous
  • anonymous
^ oh yeah u substitution :D

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anonymous
  • anonymous
@Albertoimus Do you get it? I know it looks a little messy but if you want I can rewrite so you can see it better.
anonymous
  • anonymous
by all means.
anonymous
  • anonymous
\[\int\limits_{}^{}\frac{\cos \sqrt{x}}{\sqrt{x}}dx\] where we say that \[u=\sqrt{x}\]and if we square both sides that means that \[x=u^2\]and if we take the derivative of that we get \[dx=2u\]
anonymous
  • anonymous
The next step is a matter of replacing things
anonymous
  • anonymous
woops the last part should be \[dx=2udu\]
anonymous
  • anonymous
\[\int\limits_{}^{}\frac{cosu}{u}*2udu\] we cancel the u on the top with the u on the bottom. Also since 2 is a constant we take it outside the integral \[2\int\limits_{}^{}cosu*du\] the integral of cos u du is simply sin u \[2* \sin u\] And now we want it to convert it back into x instead of u and we know already that \[u=\sqrt{x}\] So it comes out as \[2*\sin \sqrt{x}\]
anonymous
  • anonymous
Done!
anonymous
  • anonymous
thanks

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