Substitution and Integration by Parts

  • Thread starter sashab
  • Start date
  • #1
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Homework Statement


First make a substitution and then use integration by parts to evaluate the integral.

∫x[itex]^{7}[/itex]cos(x[itex]^{4}[/itex])dx

Homework Equations



Equation for Substitution: ∫f(g(x))g'(x)dx = ∫f(u)du
Equation for Integration by Parts: ∫udv = uv - ∫vdu

The Attempt at a Solution



So here's my attempted solution
tumblr_n1aepoItwY1tsd2vco1_500.jpg


I made a substitution and tried using integration by parts twice but I got stuck on the last line since it turns out to be zero... I know I went wrong somewhere but I can't seem to find my mistake. Any help would be really appreciated! Thanks :)
 

Answers and Replies

  • #2
CAF123
Gold Member
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The second line is incorrect - when you made the u substitution you did not use your expression for dx in terms of du.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
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Start by writing the integral as [itex]\int x^4cos(x^4)(x^3dx)[/itex] and it is clearer.
 
  • #4
12
0
I see my mistake now! Thanks for the help :)
 

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