What is the integral of (e^x)/(sqrt(e^x-5)) ?

The integral of (e^x)/(sqrt(e^x-5)) is 2sqrt(e^x-5)+C

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integral of (e^x)/(sqrt(e^x-5))

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

2 e^{x} - 5 + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u - 5} d u

= \int \frac{1}{u - 5} d u

Apply u-substitution

: \int 2 d v

= \int 2 d v

Integral of a constant:

\int a d x = a x

= 2 v

Substitute back

= 2 e^{x} - 5

Add a constant to the solution

= 2 e^{x} - 5 + C

\int \frac{1}{81 - x ^{2}} d x

\frac{d}{d x} ((2 + x sin (3 x))^{10})

\frac{d}{d x} ((sin^{2} (x) + 1)^{x})

4 t

\frac{d}{d x} (sin^{3} (3 x - 1))

What is the integral of (e^x)/(sqrt(e^x-5)) ?
The integral of (e^x)/(sqrt(e^x-5)) is 2sqrt(e^x-5)+C