anonymous
  • anonymous
Use U-Substitution to evaluate the Integral:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
u=(x^{4} + 3x^{2} +5)
anonymous
  • anonymous
\[\int\limits_{?}^{?} (4x^{3} +6x) \cos (x^{4} + 3x^{2} + 5 ) dx\]
anonymous
  • anonymous
I have to integrate that above this post with the U given in the first post. Please confirm my answer if you can!!

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anonymous
  • anonymous
Actually I couldn't get an answer - please helpz!!!
anonymous
  • anonymous
= sin ( u ) = sin ( x^4 + 3x^3 + 5) + C
anonymous
  • anonymous
sorry the second x should be squared ( 3x^2)
anonymous
  • anonymous
because u = x^4 + 3x^3 + 5 ==> du/dx = 4x^3 + 6x solve for dx and plug the equation for dx into the integral
anonymous
  • anonymous
if you write that out you will notice you have 4x^3 + 6x in the numerator and denominator and that equals 1. but you are still multiplying by du. because you had to solve for dx
anonymous
  • anonymous
you get \[\int\limits_{?}^{?}\cos u du\] = sin u then just plug u back into the sing
anonymous
  • anonymous
taking a step back when you solve for dx you should get dx = du / (4x^3 + 6x) plug that into the integral. you are integrating du with respect to u
anonymous
  • anonymous
\[\sin(x^{4} + 3x^{2} + 5) + c \]
anonymous
  • anonymous
perfect
anonymous
  • anonymous
awesome!! thank you so much!!
anonymous
  • anonymous
yeahp!

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