Evaluate the indefinite integral. cos^3(15x)sin^6(15x)dx?

Evaluate the indefinite integral.

cos^3(15x)sin^6(15x)dx

2 Answers

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  • 10 years ago
    Best Answer

    ∫cos^3(15x)sin^6(15x)dx =

    (1/15)∫(1 - sin^2(15x)) sin^6(15x) d(sin(15x)) =

    (1/15) ∫(sin^6(15x) d(sin(15x)) - (1/15) ∫ (sin^8(15x)d(sin(15x)) =

    (1/105)sin^7(15x) - (1/135)sin^9(15x)+C

  • 10 years ago

    Let u = sin(15x).

    du = 15*cos(15x)dx.

    Also, cos^3(15x) = cos(15x)*cos^2(15x) = cos(15x)*(1-sin^2(15x))

    So,

    cos^3(15x)sin^6(15x)dx = cos(15x) * (1-sin^2(15x)) * sin^6(15x) dx

    = (1-sin^2(15x)) * sin^6(15x) * cos(15x)dx

    = (1-u^2) * u^6 * du/15

    = (u^6 - u^8) * du/15

    Easy to integrate from here and substitute back for u=sin(15x).

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