What is the integral of (e^{2x})/(e^{2x)+7} ?

The integral of (e^{2x})/(e^{2x)+7} is 1/2 ln|e^{2x}+7|+C

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integral of (e^{2x})/(e^{2x)+7}

\int \frac{e ^{2 x}}{e ^{2 x} + 7} d x

\frac{1}{2} ln e^{2 x} + 7 + C

Solution steps

\int \frac{e ^{2 x}}{e ^{2 x} + 7} d x

Apply u-substitution

: \int \frac{1}{2 u} d u

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = e^{2 x} + 7

= \frac{1}{2} ln e^{2 x} + 7

Add a constant to the solution

= \frac{1}{2} ln e^{2 x} + 7 + C

f (x) = \frac{x}{2 x - 1}

\frac{d}{d x} (\frac{x - 3}{2 x ^{2} e ^{x}})

\int_{0}^{l n (2)} e^{x} d x

x \frac{d y}{d x} - y = x^{2}

\int_{1}^{2} \frac{ln ( x )}{x ^{2}} d x

What is the integral of (e^{2x})/(e^{2x)+7} ?
The integral of (e^{2x})/(e^{2x)+7} is 1/2 ln|e^{2x}+7|+C