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Popular >

integral of (e^{2x})/(e^{2x)+8}

Solution

\int \frac{e ^{2 x}}{e ^{2 x} + 8} d x

Solution

\frac{1}{2} ln e^{2 x} + 8 + C

Solution steps

\int \frac{e ^{2 x}}{e ^{2 x} + 8} 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} + 8

= \frac{1}{2} ln e^{2 x} + 8

Add a constant to the solution

= \frac{1}{2} ln e^{2 x} + 8 + C

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\int e^{t} \frac{1}{t} d t

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\int (x^{2} - sec^{2} (x)) d x

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\int e^{x} (2 x - 1) d x

Frequently Asked Questions (FAQ)

What is the integral of (e^{2x})/(e^{2x)+8} ?
The integral of (e^{2x})/(e^{2x)+8} is 1/2 ln|e^{2x}+8|+C