What is the integral of (e^{3x})/(5+e^{3x)} ?

The integral of (e^{3x})/(5+e^{3x)} is 1/3 ln|5+e^{3x}|+C

Popular >

integral of (e^{3x})/(5+e^{3x)}

\int \frac{e ^{3 x}}{5 + e ^{3 x}} d x

\frac{1}{3} ln 5 + e^{3 x} + C

Solution steps

\int \frac{e ^{3 x}}{5 + e ^{3 x}} d x

Apply u-substitution

: \int \frac{1}{3 u} d u

= \int \frac{1}{3 u} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} ln ∣ u ∣

Substitute back

u = 5 + e^{3 x}

= \frac{1}{3} ln 5 + e^{3 x}

Add a constant to the solution

= \frac{1}{3} ln 5 + e^{3 x} + C

\frac{d}{d x} (arccsc (- 6 x^{2}))

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

\int u^{5} d u

f (x) = \frac{x ( 2 - ln ( 2 ) x )}{2 ^{x}}

\frac{d}{d x} (\frac{x + 1}{4})

What is the integral of (e^{3x})/(5+e^{3x)} ?
The integral of (e^{3x})/(5+e^{3x)} is 1/3 ln|5+e^{3x}|+C