What is the integral from 0 to 1 of (e^x+7)/(e^x+7x) ?

The integral from 0 to 1 of (e^x+7)/(e^x+7x) is ln(e+7)

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integral from 0 to 1 of (e^x+7)/(e^x+7x)

\int_{0}^{1} \frac{e ^{x} + 7}{e ^{x} + 7 x} d x

ln (e + 7)

Decimal

2.27400 \dots

Solution steps

\int_{0}^{1} \frac{e ^{x} + 7}{e ^{x} + 7 x} d x

Apply u-substitution

= \int_{1}^{e + 7} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{e + 7}

Compute the boundaries:

ln (e + 7)

= ln (e + 7)

What is the integral from 0 to 1 of (e^x+7)/(e^x+7x) ?
The integral from 0 to 1 of (e^x+7)/(e^x+7x) is ln(e+7)