What is the integral of e^yy^2 ?

The integral of e^yy^2 is y^2e^y-2(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 e^yy^2

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

y^{2} e^{y} - 2 (e^{y} y - e^{y}) + C

Solution steps

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

Apply Integration By Parts

: y^{2} e^{y} - \int 2 y e^{y} d y

= y^{2} e^{y} - \int 2 y e^{y} d y

\int 2 y e^{y} d y = 2 (e^{y} y - e^{y})

= y^{2} e^{y} - 2 (e^{y} y - e^{y})

Add a constant to the solution

= y^{2} e^{y} - 2 (e^{y} y - e^{y}) + C

\frac{\partial}{\partial x} (9 x e^{x + y})

y^{^{''}} + 4 y^{^{'}} + 5 y = - 5 x + 5 e^{- x}

\int \frac{3}{2} e^{2 x} d x

x y^{^{'}} + y = y^{2}, y (1) = - 5

(4 e^{2 x})^{^{'}}