What is the integral of (e^z+1)/(e^z+z) ?

The integral of (e^z+1)/(e^z+z) is ln|e^z+z|+C

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integral of (e^z+1)/(e^z+z)

\int \frac{e ^{z} + 1}{e ^{z} + z} d z

ln ∣ e^{z} + z ∣ + C

Solution steps

\int \frac{e ^{z} + 1}{e ^{z} + z} d z

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = e^{z} + z

= ln ∣ e^{z} + z ∣

Add a constant to the solution

= ln ∣ e^{z} + z ∣ + C

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What is the integral of (e^z+1)/(e^z+z) ?
The integral of (e^z+1)/(e^z+z) is ln|e^z+z|+C