What is the integral of 1/(sqrt(e^x-1)) ?

The integral of 1/(sqrt(e^x-1)) is 2arctan(sqrt(e^x-1))+C

Popular >

integral of 1/(sqrt(e^x-1))

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

2 arctan (e^{x} - 1) + C

Solution steps

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

Apply u-substitution

: \int \frac{2}{u ^{2} + 1} d u

= \int \frac{2}{u ^{2} + 1} d u

Take the constant out:

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

= 2 \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= 2 arctan (u)

Substitute back

u = e^{x} - 1

= 2 arctan (e^{x} - 1)

Add a constant to the solution

= 2 arctan (e^{x} - 1) + C

y^{^{''}} - 4 y^{^{'}} - 12 y = sin (2 x)

f (x) = \frac{2}{x - 2}, at x = - 4

x \to 0 lim (\frac{cos ( x ) - x}{x})

y = x^{3}, y = x^{\frac{1}{2}}

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

What is the integral of 1/(sqrt(e^x-1)) ?
The integral of 1/(sqrt(e^x-1)) is 2arctan(sqrt(e^x-1))+C