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

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

Popular >

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

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

\frac{1}{2} ln 3 + e^{2 x} + C

Solution steps

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

Apply u-substitution

= \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 + e^{2 x}

= \frac{1}{2} ln 3 + e^{2 x}

Add a constant to the solution

= \frac{1}{2} ln 3 + e^{2 x} + C

\int \frac{1 + x + x ^{2}}{x + x ^{3}} d x

\int \frac{x ^{4} - 2 x ^{3} - 27}{x ( x ^{2} + 9 ) ^{2}} d x

\int x^{5} - \frac{1}{x} + e^{x} d x

\int \frac{( x + 2 ) ^{2}}{x} d x

\int sin^{3} (y) cos^{4} (y) d y

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