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)}

integral

e^{(2 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 \frac{sin ( h ) 7 x}{1 + cos ( h ^{2} ) 7 x} d x

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

\int x^{2} (5 x + 8)^{\frac{1}{2}} d x

\int e^{2 x} cos (3 x + 1) d x

\int \frac{2}{3} (1 - x^{2})^{\frac{3}{2}} d x