Get the solution to "Integrals Evaluate the following integrals. Include absolute values..."

Yasmin

Answered question

2021-10-20

Integrals Evaluate the following integrals. Include absolute values only when needed.

\int \frac{e^{2 x}}{4 + e^{2 x}} d x

hosentak

Skilled2021-10-21Added 100 answers

Given,

\int \frac{e^{2 x}}{4 + e^{2 x}} d x

Put,

4 + e^{2 x} = t

\Rightarrow 0 + 2 e^{2 x} = \frac{d t}{d x}

\Rightarrow 2 e^{2 x} d x = d t

\Rightarrow e^{2 x} d x = \frac{d t}{2}

Therefore integral becomes,

\int \frac{e^{2 x}}{4 + e^{2 x}} d x = \int \frac{\frac{d t}{2}}{t}

= \frac{1}{2} \int \frac{d t}{t}

= \frac{1}{2} \ln | t | + C

= \frac{1}{2} \ln | 4 + e^{2 x} | + C

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