What is the integral from 0 to 1 of (e^z+3)/(e^z+3z) ?

The integral from 0 to 1 of (e^z+3)/(e^z+3z) is ln(e+3)

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integral from 0 to 1 of (e^z+3)/(e^z+3z)

\int_{0}^{1} \frac{e ^{z} + 3}{e ^{z} + 3 z} d z

ln (e + 3)

Solution steps

\int_{0}^{1} \frac{e ^{z} + 3}{e ^{z} + 3 z} d z

Apply u-substitution

: \int_{1}^{e + 3} \frac{1}{u} d u

= \int_{1}^{e + 3} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{e + 3}

Compute the boundaries:

ln (e + 3)

= ln (e + 3)

\int_{3}^{4} t^{2} - 2 t - 3 d t

\int_{0}^{1} 3^{x} d x

\int_{- π}^{0} - sin (x) d x

\int_{1}^{2} \frac{1}{2} d x

\int_{0}^{2} - x^{2} - 3 x d x

What is the integral from 0 to 1 of (e^z+3)/(e^z+3z) ?
The integral from 0 to 1 of (e^z+3)/(e^z+3z) is ln(e+3)