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integral

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find the integral

~(e^x + x)^2 (e^x + 1)dx


can you pls explain how it arrive to this?

ans = 2e^4x + C

  • integral -

    integral( (e^x+ x)^2 * (e^x + 1) dx )

    let u = e^x + x
    du = (e^x + 1)dx

    Now you have integral(u^2 du)
    = (u^3)/3 +C
    = ((e^x + x)^3)/3 +C
    = (e^3x + 3x*e^2x + 3x^2*e^x + x^3)/3 +C

    Are you looking at the right answer key?

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