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

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

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

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

ln (e + 3)

Decimal

1.74366 \dots

Solution steps

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

Apply u-substitution

= \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)

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