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Kris
Lv 5
Kris asked in Science & MathematicsMathematics · 9 years ago

How would I take the integral of e^(2x) * square root (e^x + 1)?

Please help me! The answer is (2/5)e^(5/2x) - 5e^(3/2x) + c

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  • MechEng2030
    Lv 7
    9 years ago

    ∫e^(2x)*√(e^(x) + 1) dx

    Make the substitution:

    u = e^(x) + 1

    du = e^(x) dx

    ∫(u - 1)*√u du

    ∫(u^(3/2) - √u) du

    = 2/5*u^(5/2) - 2/3*u^(3/2) + C

    = 2/5*(e^(x) + 1)^(5/2) - 2/3*(e^(x) + 1)^(3/2) + C

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