What is the integral of (e^x)/(3+2e^x) ?

The integral of (e^x)/(3+2e^x) is 1/2 ln|3+2e^x|+C

Popular >

integral of (e^x)/(3+2e^x)

\int \frac{e ^{x}}{3 + 2 e ^{x}} d x

\frac{1}{2} ln ∣ 3 + 2 e^{x} ∣ + C

Solution steps

\int \frac{e ^{x}}{3 + 2 e ^{x}} 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 = 3 + 2 e^{x}

= \frac{1}{2} ln ∣ 3 + 2 e^{x} ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ 3 + 2 e^{x} ∣ + C

\int \frac{( x - 9 ) ^{6}}{2 x} d x

\int \frac{3}{x ^{2} + 5} d x

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

\int \frac{1 - x}{2 x - x ^{2}} d x

\int sin (t) + 1 d t

What is the integral of (e^x)/(3+2e^x) ?
The integral of (e^x)/(3+2e^x) is 1/2 ln|3+2e^x|+C