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Math Help - Indefinite integrals

  1. #1
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    Indefinite integrals

    Hi

    I have to find the indefinite integral of:

    f(t) = 6cos(3t)+5e^-10t

    can anyone please show me step by step how to work this out.

    many thanks
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  2. #2
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    Quote Originally Posted by tracy207 View Post
    Hi

    I have to find the indefinite integral of:

    f(t) = 6cos(3t)+5e^-10t

    can anyone please show me step by step how to work this out.

    many thanks
    \int f(t)~dt = 6 \int cos(3t)~dt + \int e^{-10t}~dt

    The first integral may be found by substituting u = 3t \implies du = 3 dt:
    \int cos(3t)~dt = \int cos(u) \cdot \frac{du}{3} = \frac{1}{3} \int cos(u)~du = \frac{1}{3} \cdot sin(u) = \frac{1}{3} \cdot sin(3t)

    For the second integral, use u = -10t \implies du = -10 dt.

    You give this part a try. (And, of course, don't leave out that arbitrary constant at the end.)

    -Dan
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