What is the integral from 0 to 1 of (e^x)/(4-e^{2x)} ?

The integral from 0 to 1 of (e^x)/(4-e^{2x)} is diverges

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integral from 0 to 1 of (e^x)/(4-e^{2x)}

\int_{0}^{1} \frac{e ^{x}}{4 - e ^{2 x}} d x

diverges

Solution steps

\int_{0}^{1} \frac{e ^{x}}{4 - e ^{2 x}} d x

Find undefined (singularity) points:

x = ln (2)

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{0}^{l n (2)} \frac{e ^{x}}{4 - e ^{2 x}} d x + \int_{l n (2)}^{1} \frac{e ^{x}}{4 - e ^{2 x}} d x

\int_{0}^{l n (2)} \frac{e ^{x}}{4 - e ^{2 x}} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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What is the integral from 0 to 1 of (e^x)/(4-e^{2x)} ?
The integral from 0 to 1 of (e^x)/(4-e^{2x)} is diverges