What is the integral of (e^{4x})/(e^{4x)-8} ?

The integral of (e^{4x})/(e^{4x)-8} is 1/4 ln|e^{4x}-8|+C

Popular >

integral of (e^{4x})/(e^{4x)-8}

\int \frac{e ^{4 x}}{e ^{4 x} - 8} d x

\frac{1}{4} ln e^{4 x} - 8 + C

Solution steps

\int \frac{e ^{4 x}}{e ^{4 x} - 8} d x

Apply u-substitution

: \int \frac{1}{4 u} d u

= \int \frac{1}{4 u} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{4} ln ∣ u ∣

Substitute back

u = e^{4 x} - 8

= \frac{1}{4} ln e^{4 x} - 8

Add a constant to the solution

= \frac{1}{4} ln e^{4 x} - 8 + C

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

\int \frac{x ^{4} + 3 x ^{2} + 3}{x ^{2} + 1} d x

\int (x^{2} - 4 x)^{5} \cdot (4 x - 8) d x

\int \frac{1}{1 + u} d u

\int π^{2} cos (n x) d x

What is the integral of (e^{4x})/(e^{4x)-8} ?
The integral of (e^{4x})/(e^{4x)-8} is 1/4 ln|e^{4x}-8|+C