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

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

Popular >

integral of y/(e^{y^2)}

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

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

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

Apply u-substitution

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

= \int - \frac{e ^{u}}{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 = - y^{2}

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

Add a constant to the solution

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

\int (3 x^{3} - 5 x^{2} + 4) d x

\int \frac{1 - 3 x}{2 x - 3 x ^{2}} d x

\int (x^{5} - π^{5} + x^{2} - π^{2}) d x

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

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

What is the integral of y/(e^{y^2)} ?
The integral of y/(e^{y^2)} is -1/2 e^{-y^2}+C