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Maths - Integration by parts

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Integral x^2 sin(x) dx

  • Maths - Integration by parts -

    Let I = ∫x^2 sinx dx

    u = x^2
    du = 2x dx

    dv = sinx
    v = -cosx

    ∫u dv = uv - ∫v du
    = -x^2 cosx + ∫2x cosx dx

    now, for ∫x cosx dx,

    u = x
    du = dx

    dv = cosx dx
    v = sinx

    I = -x^2 cosx + 2(x sinx - ∫sinx dx)
    = -x^2 cosx + 2x sinx + 2cosx + C
    = 2x sinx + (2-x^2)cosx + C

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