What is the integral of-e^yy^2 ?

The integral of-e^yy^2 is -e^yy^2+2e^yy-2e^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

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

Solution steps

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

Take the constant out:

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

= - \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}))

Simplify

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

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

Add a constant to the solution

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

x + 2

x - 2

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

\int \frac{1}{( x ^{2} + 2 x + 2 ) ^{\frac{3}{2}}} d x

\int \frac{1}{x ^{\frac{1}{n}}} d x