What is the integral of e^{(5x)/2} ?

The integral of e^{(5x)/2} is 2/5 e^{(5x)/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{(5x)/2}

\int e^{\frac{5 x}{2}} d x

\frac{2}{5} e^{\frac{5 x}{2}} + C

Solution steps

\int e^{\frac{5 x}{2}} d x

Apply u-substitution

: \int e^{u} \frac{2}{5} d u

= \int e^{u} \frac{2}{5} d u

Take the constant out:

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

= \frac{2}{5} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{2}{5} e^{u}

Substitute back

u = \frac{5 x}{2}

= \frac{2}{5} e^{\frac{5 x}{2}}

Add a constant to the solution

= \frac{2}{5} e^{\frac{5 x}{2}} + C

\int x d x d x

\int \frac{17 x + 4}{3 x ^{2} - 7 x - 6} d x

\int 2 x - \frac{1}{5} d x

\int x e^{2 y} d x

\int x e^{- j w x} d x

What is the integral of e^{(5x)/2} ?
The integral of e^{(5x)/2} is 2/5 e^{(5x)/2}+C