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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 8e^{5x+e^{5x}}

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

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

Solution steps

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

Take the constant out:

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

= 8 \cdot \int e^{5 x + e^{5 x}} d x

Apply u-substitution

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

= 8 \cdot \int e^{u + 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

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

Apply u-substitution

: \int e^{v} d v

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

Use the common integral:

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

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

Substitute back

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

Simplify

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

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

Add a constant to the solution

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

\int cot^{2} (x) csc^{6} (x) d x

\frac{x ^{2.3} + 4}{x ^{3.5} + 1}

\int w ln (w) d w

y^{^{'}} + \frac{3}{2 x} y = 0

\int_{1}^{5} (4 x - 1) d x

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