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Calculus 1

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Evaluate the definite integral: (dx/(x(1+ln(x))) from 1 to e^7.

  • Calculus 1 - ,

    let u = lnx
    then du = dx/x

    ∫1/[x*(lnx+1] dx
    = ∫(1/(u+1) du
    = ln(u+1) + C
    = ln[lnx+1)] + C

    When x = 1, the indefinite integral is 0
    When x =e^7, the indefinite integral is ln8. The C terms can be ignored since they cancel out.

    ln8 is the answer

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