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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{x/8}

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

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

Solution steps

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

Apply u-substitution

: \int e^{u} \cdot 8 d u

= \int e^{u} \cdot 8 d u

Take the constant out:

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

= 8 \cdot \int e^{u} d u

Use the common integral:

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

= 8 e^{u}

Substitute back

u = \frac{x}{8}

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

Add a constant to the solution

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

sin (2 x), cos (x), [\frac{π}{6}, \frac{π}{2}]

y = - ln (x)

x \to 0 lim (\frac{sin ( 8 x )}{sin ( 7 x )})

\frac{d}{d x} (x^{2} + y)

\frac{\partial}{\partial x} (arccos (\frac{y}{x}))