What is the integral of e^{13x}(13) ?

The integral of e^{13x}(13) is e^{13x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{13x}(13)

\int e^{13 x} (13) d x

e^{13 x} + C

Solution steps

\int e^{13 x} \cdot 13 d x

Take the constant out:

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

= 13 \cdot \int e^{13 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{13} d u

= 13 \cdot \int e^{u} \frac{1}{13} d u

Take the constant out:

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

= 13 \cdot \frac{1}{13} \cdot \int e^{u} d u

Use the common integral:

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

= 13 \cdot \frac{1}{13} e^{u}

Substitute back

u = 13 x

= 13 \cdot \frac{1}{13} e^{13 x}

Simplify

13 \cdot \frac{1}{13} e^{13 x} : e^{13 x}

= e^{13 x}

Add a constant to the solution

= e^{13 x} + C

\int 16 cos^{2} (t) d t

x \to 3 lim (\frac{x}{3 - x})

f (x) = 5 x - 3

\int (x + 5) d x

\frac{d}{d x} (\frac{x ^{3} + 6}{x})