What is the integral of ke^{3x} ?

The integral of ke^{3x} is k 1/3 e^{3x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ke^{3x}

\int k e^{3 x} d x

k \frac{1}{3} e^{3 x} + C

Solution steps

\int k e^{3 x} d x

Take the constant out:

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

= k \cdot \int e^{3 x} d x

Apply u-substitution

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

= k \cdot \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

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

Use the common integral:

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

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

Substitute back

u = 3 x

= k \frac{1}{3} e^{3 x}

Add a constant to the solution

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

\frac{d}{d x} (x + 5 sin (x))

x \to 5 - lim (\frac{3}{x ^{2} - 25})

f (x) = 19 e^{x^{2}}

f (x) = e^{e^{x}}

y \cdot e^{2 x} d x = (1 + e^{2 x}) d y