en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of y+xe^y

Solution

\int y + x e^{y} d y

Solution

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

Solution steps

\int y + x e^{y} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int y d y + \int x e^{y} d y

\int y d y = \frac{y ^{2}}{2}

\int x e^{y} d y = x e^{y}

= \frac{y ^{2}}{2} + x e^{y}

Add a constant to the solution

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

Graph

Popular Examples

limit as x approaches infinity of 1*x

derivative of (x^3-8/(x^3+8))

derivative of tan(ax+b)

x^2y^{''}=y^'+(y^')^2

(\partial)/(\partial x)(x^{xy})

Frequently Asked Questions (FAQ)

What is the integral of y+xe^y ?
The integral of y+xe^y is (y^2)/2+xe^y+C