What is the integral of e^{(3x)/2} ?

The integral of e^{(3x)/2} is 2/3 e^{(3x)/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^{(3x)/2}

\int e^{\frac{3 x}{2}} d x

\frac{2}{3} e^{\frac{3 x}{2}} + C

Solution steps

\int e^{\frac{3 x}{2}} d x

Apply u-substitution

: \int e^{u} \frac{2}{3} d u

= \int e^{u} \frac{2}{3} d u

Take the constant out:

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

= \frac{2}{3} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{2}{3} e^{u}

Substitute back

u = \frac{3 x}{2}

= \frac{2}{3} e^{\frac{3 x}{2}}

Add a constant to the solution

= \frac{2}{3} e^{\frac{3 x}{2}} + C

n = 1 \sum \infty \frac{n + 2}{3 n + 4}

\int e^{- kn x} + e^{- l n (x)} d x

\int \frac{x ^{3}}{x ^{2} - 49} d x

9 y^{^{''}} + 30 y^{^{'}} + 25 y = 0

What is the integral of e^{(3x)/2} ?
The integral of e^{(3x)/2} is 2/3 e^{(3x)/2}+C