- #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

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- Thread starter mckallin
- Start date

- #1

- 15

- 0

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

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

- #2

mjsd

Homework Helper

- 726

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hint: try look for a substitution to make the integrand look nicer, then you can try by parts.

- #3

- 15

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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

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try

[tex]u=x^3,dv=x^2\cos(x^3)dx[/tex]

have you learned partial substitution ?

[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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