What is the integral of (e^{2x})/(e^{2x)+5} ?

The integral of (e^{2x})/(e^{2x)+5} is 1/2 ln|e^{2x}+5|+C

Popular >

integral of (e^{2x})/(e^{2x)+5}

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

\frac{1}{2} ln e^{2 x} + 5 + C

Solution steps

\int \frac{e ^{2 x}}{e ^{2 x} + 5} 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} + 5

= \frac{1}{2} ln e^{2 x} + 5

Add a constant to the solution

= \frac{1}{2} ln e^{2 x} + 5 + C

\frac{1 - 2 x}{3 + x}

\frac{d}{d x} (\frac{x ^{5}}{( x ^{2} + 1 ) ( x ^{3} + 4 )})

\frac{d}{d x} (m sin (2 (m x + n y (x))))

x^{2} tan (x)

x \to + 0 lim (\frac{tan ( 6 x )}{sin ( 4 x )})

What is the integral of (e^{2x})/(e^{2x)+5} ?
The integral of (e^{2x})/(e^{2x)+5} is 1/2 ln|e^{2x}+5|+C