What is the integral of (e^x)/((5-e^x)^2) ?

The integral of (e^x)/((5-e^x)^2) is 1/(5-e^x)+C

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integral of (e^x)/((5-e^x)^2)

\int \frac{e ^{x}}{( 5 - e ^{x} ) ^{2}} d x

\frac{1}{5 - e ^{x}} + C

Solution steps

\int \frac{e ^{x}}{( 5 - e ^{x} ) ^{2}} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Apply the Power Rule

: - \frac{1}{u}

= - (- \frac{1}{u})

Substitute back

u = 5 - e^{x}

= - (- \frac{1}{5 - e ^{x}})

Simplify

= \frac{1}{5 - e ^{x}}

Add a constant to the solution

= \frac{1}{5 - e ^{x}} + C

\int sin (x) e^{- s x} d x

\int \frac{1}{v ^{2} - v + 1} d v

f (x) = ln (\frac{x + 1}{x - 1})

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

5 x^{2} + 4 x + 2

What is the integral of (e^x)/((5-e^x)^2) ?
The integral of (e^x)/((5-e^x)^2) is 1/(5-e^x)+C