What is the integral of (2+x+ye^y) ?

The integral of (2+x+ye^y) is 2y+xy+e^yy-e^y+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2+x+ye^y)

\int (2 + x + y e^{y}) d y

2 y + x y + e^{y} y - e^{y} + C

Solution steps

\int 2 + x + y 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 2 d y + \int x d y + \int e^{y} y d y

\int 2 d y = 2 y

\int x d y = x y

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

= 2 y + x y + e^{y} y - e^{y}

Add a constant to the solution

= 2 y + x y + e^{y} y - e^{y} + C

\int \frac{x}{( x ^{2} + 1 ) 1 - x ^{2}} d x

\int \frac{1}{( 5 x + 2 ) ^{4}} d x

\int (e^{x} + e^{- x})^{- 1} d x

\int \frac{1}{- sin ( x )} d x

\int (x^{5} + 8) d x

What is the integral of (2+x+ye^y) ?
The integral of (2+x+ye^y) is 2y+xy+e^yy-e^y+C