What is the integral of (e^xln(e^x-w))/(e^x-w) ?

The integral of (e^xln(e^x-w))/(e^x-w) is (ln^2(-w+e^x))/2+C

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integral of (e^xln(e^x-w))/(e^x-w)

\int \frac{e ^{x} ln ( e ^{x} - w )}{e ^{x} - w} d x

\frac{ln ^{2} ( - w + e ^{x} )}{2} + C

Solution steps

\int \frac{e ^{x} ln ( e ^{x} - w )}{e ^{x} - w} d x

Apply u-substitution

: \int \frac{ln ( u )}{u} d u

= \int \frac{ln ( u )}{u} d u

Apply u-substitution

: \int v d v

= \int v d v

Apply the Power Rule

: \frac{v ^{2}}{2}

= \frac{v ^{2}}{2}

Substitute back

= \frac{ln ^{2} ( - w + e ^{x} )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( - w + e ^{x} )}{2} + C

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What is the integral of (e^xln(e^x-w))/(e^x-w) ?
The integral of (e^xln(e^x-w))/(e^x-w) is (ln^2(-w+e^x))/2+C