What is the integral of 5e^{8x} ?

The integral of 5e^{8x} is 5/8 e^{8x}+C

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integral of 5e^{8x}

\int 5 e^{8 x} d x

\frac{5}{8} e^{8 x} + C

Solution steps

\int 5 e^{8 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^{8 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{8} d u

= 5 \cdot \int e^{u} \frac{1}{8} d u

Take the constant out:

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

= 5 \cdot \frac{1}{8} \cdot \int e^{u} d u

Use the common integral:

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

= 5 \cdot \frac{1}{8} e^{u}

Substitute back

u = 8 x

= 5 \cdot \frac{1}{8} e^{8 x}

Simplify

5 \cdot \frac{1}{8} e^{8 x} : \frac{5}{8} e^{8 x}

= \frac{5}{8} e^{8 x}

Add a constant to the solution

= \frac{5}{8} e^{8 x} + C

(cos (x))^{^{'}}

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

x \to 3 lim ([3 (8) (- 10)])

\int \frac{8}{t + 1} + t d t

\frac{d}{d x} (e^{x y}) = \frac{d}{d x} (2 y)