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anonymous

  • 4 years ago

Calculas help? ∫??(5−ex)(e2x)dx

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  1. anonymous
    • 4 years ago
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    \[\int\limits_{?}^{?}(5-e ^{x})(e ^{2x})\]

  2. bahrom7893
    • 4 years ago
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    Multiply it out, it's gonna make your life much easier

  3. bahrom7893
    • 4 years ago
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    Int (5e^(2x)-e^(3x),x)

  4. anonymous
    • 4 years ago
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    opps it is suppose to be divided by the second e

  5. bahrom7893
    • 4 years ago
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    ohh that makes it a little different

  6. anonymous
    • 4 years ago
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    yea i would think so lol

  7. bahrom7893
    • 4 years ago
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    oh still rewrite it as: Int (5/e^(2x) - e^x/e^(2x))) Int (5*e^(-2x) - e^(-x))

  8. bahrom7893
    • 4 years ago
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    Now split it into two: 5 * Int(e^(-2x)) - Int(e^(-x))

  9. bahrom7893
    • 4 years ago
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    Now just use the rule: Int (e^(kx)) = e^(kx) / k

  10. bahrom7893
    • 4 years ago
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    In the first half k = -2, in the second half, k = -1 So finally: 5 * (e^(-2x)/(-2)) + e^(-x) + C

  11. anonymous
    • 4 years ago
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    ok that makes sense thanks

  12. bahrom7893
    • 4 years ago
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    btw to prove that Int (e^(kx)) = e^(kx)/k just use u sub. Let u = kx, du = k dx, etc..

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