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

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

Popular >

integral of 5/(e^x)

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

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

Solution steps

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

Take the constant out:

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

= 5 \cdot \int \frac{1}{e ^{x}} d x

Apply u-substitution

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

= 5 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 5 (- \frac{1}{u})

Substitute back

u = e^{x}

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

Simplify

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

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

Add a constant to the solution

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

\int sin (2 x) cos (\frac{x}{3}) d x

\int (x^{\frac{4}{3}} - 4 x^{\frac{1}{3}}) d x

\int \frac{3 + 12 z}{2 z ^{2} + z + 1} d z

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

\int \frac{4 x + 5}{2 x} + e^{x} d x