What is the integral of e^{5t} ?

The integral of e^{5t} is 1/5 e^{5t}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{5t}

\int e^{5 t} d t

\frac{1}{5} e^{5 t} + C

Solution steps

\int e^{5 t} d t

Apply u-substitution

: \int e^{u} \frac{1}{5} d u

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = 5 t

= \frac{1}{5} e^{5 t}

Add a constant to the solution

= \frac{1}{5} e^{5 t} + C

arctan (4 x)

\int \frac{2}{8 - 5 x} d x

f (x) = x^{\frac{1}{2}} (x^{2} - x + 3), at x = 1

(27 + x^{2}) y^{^{'}} - 2 x y = 0

\int (\frac{x}{10})^{n} d x