What is the integral of e^{3x-5} ?

The integral of e^{3x-5} is 1/3 e^{3x-5}+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-5}

\int e^{3 x - 5} d x

\frac{1}{3} e^{3 x - 5} + C

Solution steps

\int e^{3 x - 5} d x

Apply u-substitution

: \int e^{u} \frac{1}{3} d u

= \int e^{u} \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{3} e^{u}

Substitute back

u = 3 x - 5

= \frac{1}{3} e^{3 x - 5}

Add a constant to the solution

= \frac{1}{3} e^{3 x - 5} + C

\frac{d}{d x} (\frac{3 x + 1}{2 x - 5})

\int_{b}^{2 b} x^{4} d x

\frac{d}{d x} (x^{3} e^{- 3 x})

\frac{d}{d x} (5 e^{4 x} - cos^{2} (2 e^{x}))

\int sin^{2} (2 θ) d θ