What is the integral of (e^{10+3x})/5 ?

The integral of (e^{10+3x})/5 is 1/15 e^{10+3x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (e^{10+3x})/5

\int \frac{e ^{10 + 3 x}}{5} d x

\frac{1}{15} e^{10 + 3 x} + C

Solution steps

\int \frac{e ^{10 + 3 x}}{5} d x

Take the constant out:

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

= \frac{1}{5} \cdot \int e^{10 + 3 x} d x

Apply u-substitution

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

= \frac{1}{5} \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

= \frac{1}{5} \cdot \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{5} \cdot \frac{1}{3} e^{u}

Substitute back

u = 10 + 3 x

= \frac{1}{5} \cdot \frac{1}{3} e^{10 + 3 x}

Simplify

\frac{1}{5} \cdot \frac{1}{3} e^{10 + 3 x} : \frac{1}{15} e^{10 + 3 x}

= \frac{1}{15} e^{10 + 3 x}

Add a constant to the solution

= \frac{1}{15} e^{10 + 3 x} + C

x \to - 4 lim (- 4)

f (x) = 3 - 8 x^{2}, (- 3, - 69)

\frac{d}{d x} (arctan (3 x^{3}))

\frac{x - 1}{x + 1}

\int \frac{cos ( x )}{2 sin ( x ) + 1} d x

What is the integral of (e^{10+3x})/5 ?
The integral of (e^{10+3x})/5 is 1/15 e^{10+3x}+C