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

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

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

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

diverges

Solution steps

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

Compute the indefinite integral:

\int \frac{1}{e ^{x} + 3} d x = \frac{1}{3} x - \frac{1}{3} ln ∣ e^{x} + 3 ∣ + C

Compute the boundaries:

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

diverges

= diverges

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