What is the integral of e^{1/7 x} ?

The integral of e^{1/7 x} is 7e^{1/7 x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{1/7 x}

\int e^{\frac{1}{7} x} d x

7 e^{\frac{1}{7} x} + C

Solution steps

\int e^{\frac{1}{7} x} d x

Apply u-substitution

: \int e^{u} \cdot 7 d u

= \int e^{u} \cdot 7 d u

Take the constant out:

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

= 7 \cdot \int e^{u} d u

Use the common integral:

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

= 7 e^{u}

Substitute back

u = \frac{1}{7} x

= 7 e^{\frac{1}{7} x}

Add a constant to the solution

= 7 e^{\frac{1}{7} x} + C

\int (4 x^{3} + 8 x + 9) d x

\int (2 e^{x} + x^{2}) d x

\int x^{5} in x d x

\int \frac{12 x}{1 + 4} d x

\int \frac{5 x}{4} d x