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calculus

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How would you integrate tan5xdx ?

Thanks in advance.

Can you use u substitution?

  • calculus - ,

    try taking the derivative of
    ln(cosx)

    that should give you a good hint

  • calculus - ,

    I know you get -sin x; I know how to do the problem without the 5, but I don't understand how to do the problem since it is tangent of 5x

  • calculus - ,

    The derivative of ln(cosx) is actually
    -tanx, not -sinx. "ln" means "natural (base e) logarithm of..

    For the integral of tan 5x, let u = 5x
    tan 5x = u
    du = 5 dx

    integral of tan(5x) dx
    = integral of (1/5) tan u du
    = -(1/5)ln cos u
    = -(1/5)ln cos(5x)

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