What is the integral of e^{2x} ?

The integral of e^{2x} is 1/2 e^{2x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{2x}

\int e^{2 x} d x

\frac{1}{2} e^{2 x} + C

Solution steps

\int e^{2 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{2} d u

= \int e^{u} \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{2} e^{u}

Substitute back

u = 2 x

= \frac{1}{2} e^{2 x}

Add a constant to the solution

= \frac{1}{2} e^{2 x} + C

\int_{1}^{e^{2}} \frac{3}{x} d x

\int \frac{1}{( 2 x + 5 ) ^{2}} d x

\int \frac{1}{x ^{2} ( x - 1 ) ( x - 2 )} d x

\int \frac{x ^{4} + x - 36}{x ^{2} + 6} d x

11 x d y + 11 y d x + x d x = 0