What is the integral of e^{2y} ?

The integral of e^{2y} is 1/2 e^{2y}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{2y}

\int e^{2 y} d y

\frac{1}{2} e^{2 y} + C

Solution steps

\int e^{2 y} d y

Apply u-substitution

: \int e^{u} \frac{1}{2} d u

= \int e^{u} \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{2} e^{u}

Substitute back

u = 2 y

= \frac{1}{2} e^{2 y}

Add a constant to the solution

= \frac{1}{2} e^{2 y} + C

\frac{d y}{d x} = (3 x^{2} \cdot (1 + y^{2}))

y = x^{2} + 9

\frac{x - x}{x ^{\frac{1}{4}}}

(1 - x)^{\frac{1}{4}}, 0

\int cos (x + \frac{π}{3}) d x