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Math Help - trigonometric integrals

  1. #1
    Junior Member
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    trigonometric integrals

    i need some help with what to do when there is something inside the trig function.
    so this problem is:
    sin(x/2)^5
    i could do it, i think, if it were just sin(x). but not completely sure what to do now.
    so i change it to:
    (sin(x/2)^2)^2 *(sin(x/2)). which changes to
    (1-cos(x/2)^2)^2 *(-d(cosx). then
    (1-u^2)^2 *(-du)

    but what do i do with the inside part of this? can someone explain it or show me to solve the rest of it? or tell me what i've done wrong so far. i don't want to go through solving the rest of it because i don't know what exactly to do.
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  2. #2
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    let t = \frac{x}{2}

    dt = \frac{1}{2} \, dx

    dx = 2 \, dt

    \int \sin^5\left(\frac{x}{2}\right) \, dx

    \int \sin^5(t) \cdot 2 \, dt

    2 \int \sin^5(t) \, dt

    now do the integration
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