What is the integral of (e^{4x})/(e^{4x)+3} ?

The integral of (e^{4x})/(e^{4x)+3} is 1/4 ln|e^{4x}+3|+C

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integral of (e^{4x})/(e^{4x)+3}

\int \frac{e ^{4 x}}{e ^{4 x} + 3} d x

\frac{1}{4} ln e^{4 x} + 3 + C

Solution steps

\int \frac{e ^{4 x}}{e ^{4 x} + 3} d x

Apply u-substitution

: \int \frac{1}{4 u} d u

= \int \frac{1}{4 u} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{4} ln ∣ u ∣

Substitute back

u = e^{4 x} + 3

= \frac{1}{4} ln e^{4 x} + 3

Add a constant to the solution

= \frac{1}{4} ln e^{4 x} + 3 + C

\frac{d}{d x} (cos (x^{2}) (2 x))

5 x^{2} - 3 x + 1

\frac{d}{d x} (3 \cdot 5^{x})

x \to 3 lim (2 x^{3} - 10 x - 8)

x \to 0 lim (\frac{x ^{2} - 9}{x - 3})

What is the integral of (e^{4x})/(e^{4x)+3} ?
The integral of (e^{4x})/(e^{4x)+3} is 1/4 ln|e^{4x}+3|+C