What is the integral of 5e^{5x} ?

The integral of 5e^{5x} is e^{5x}+C

Popular >

integral of 5e^{5x}

\int 5 e^{5 x} d x

e^{5 x} + C

Solution steps

\int 5 e^{5 x} d x

Take the constant out:

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

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

Apply u-substitution

: \int e^{u} \frac{1}{5} d u

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

Take the constant out:

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

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

Use the common integral:

\int e^{u} d u = e^{u}

= 5 \cdot \frac{1}{5} e^{u}

Substitute back

u = 5 x

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

Simplify

5 \cdot \frac{1}{5} e^{5 x} : e^{5 x}

= e^{5 x}

Add a constant to the solution

= e^{5 x} + C

f (x) = - 6 x^{2} - 9, at x = 0

x \to - 4 - lim (f (x))

\frac{d}{d x} (e^{x} \cdot 2^{x})

x \to 0 lim (\frac{e ^{x} - 1}{sin ( 4 x )})

e^{- t} sin (t)