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

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

Popular >

integral of (e^{2x+1})/(e^{2x)+3}

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

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

Solution steps

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

Apply u-substitution

: \int \frac{e}{2 u} d u

= \int \frac{e}{2 u} d u

Take the constant out:

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

= \frac{e}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{e}{2} ln ∣ u ∣

Substitute back

u = e^{2 x} + 3

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

Add a constant to the solution

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

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

\int (3 x^{2} + 8 x - 4) d x

\int \frac{1}{( 1 - x ^{2} ) arcsin ( x )} d x

\int \frac{e ^{6 x}}{e ^{6 x} + 2} d x

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

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