What is the integral of e^{mx} ?

The integral of e^{mx} is 1/m e^{mx}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{mx}

\int e^{m x} d x

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

Solution steps

\int e^{m x} d x

Apply u-substitution

: \int \frac{e ^{u}}{m} d u

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{m} e^{u}

Substitute back

u = m x

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

Add a constant to the solution

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

\int \frac{- 4 x + 1}{1 - x ^{2}} d x

\int \frac{cos ( \frac{π}{x ^{27}} )}{x ^{28}} d x

\int \frac{1}{x} x^{2} + 1 d x

\int \frac{x ^{3} - 3 x + 3}{x ^{2} + x - 2} d x

\int (x^{2} + 3)^{3} x d x