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Math Help - integral x^3*cos(x^2)

  1. #1
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    integral x^3*cos(x^2)

    my sheet says integrate by substitution then by parts. feeling a little stumped by the substitution guess i should have paid a little better attention in class.

    intergal (x^3)(cos(x^2))dx
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  2. #2
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    Quote Originally Posted by kyle89 View Post
    my sheet says integrate by substitution then by parts. feeling a little stumped by the substitution guess i should have paid a little better attention in class.

    intergal (x^3)(cos(x^2))dx
    Hi

    Substitute u=x^2 \Rightarrow du = 2x\:dx

    \int x^3 \: \cos(x^2)dx = \int u \cos u \:\frac{du}{2}
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  3. #3
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    Quote Originally Posted by kyle89 View Post
    my sheet says integrate by substitution then by parts. feeling a little stumped by the substitution guess i should have paid a little better attention in class.

    intergal (x^3)(cos(x^2))dx
    Let p=x^2

    dp = 2x dx

    \int x^3 \cos(x^2)dx = \int p \cos p \:\frac{dp}{2}
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  4. #4
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    integral (x^3)cos(x^2)=(1/2)integral ucos(u)du
    let u=cos(u) du=-usin(u)
    dv=u v=1/2 u^2
    =(1/2)((1/2 u^2)cos(u)-integral (((1/2)u^2)(-usin(u))du)
    =(1/2)((1/2 u^2)cos(u)+(1/2)integral((u^2)(usin(u))du)
    =(1/2)((1/2)(((u^2)cos(u)+integral((u^3)sin(u)du)

    than what comes after that? or am i missing something here?
    also how do i make the integral sign and put things to a power?
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  5. #5
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    \int ucosudu = usinu + cosu
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