Please Help Integration!

  • Thread starter mckallin
  • Start date
  • #1
15
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Please Help!! Integration!

can anyone help me solve the following integration? thanks a lot.

[tex]\int[/tex] [tex]x^5[/tex]cos[tex](x^3)[/tex] dx
 

Answers and Replies

  • #2
mjsd
Homework Helper
726
3
you really should show some more effort. ie. show us what you have tried, what you know and tell us what you have problems with.


hint: try look for a substitution to make the integrand look nicer, then you can try by parts.
 
  • #3
15
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I have tried to do it by part.

If I make [tex] u=cos(x^3), dv=x^5 dx [/tex], the grade of x, which is in the [tex] cos(x^3) [/tex], won't be reduce.

If I make [tex] u=x^5, dv=cos(x^3) dx [/tex], I can't solve the [tex] \int cos(x^3) dx[/tex].

I have thought if there is some way to make it look nicer (like [tex]u=x^3[/tex] ),but I still can't work out a better substitution.

Could you give me some more advice?
 
  • #4
10
0
try
[tex]u=x^3,dv=x^2\cos(x^3)dx[/tex]

have you learned partial substitution ?
 
  • #5
mjsd
Homework Helper
726
3
hint: try look for a substitution to make the integrand look nicer, then you can try by parts.

here I suggested a two-step process,
substitiion: u = x^3 seems ok
then by parts in new variable

then put answer back in x.
 

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