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

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

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integral of (ye^{y^2})

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

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

Solution steps

\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

x (x - 2)

\frac{d}{d t} (\frac{a + b t + c t ^{2}}{t})

\int tan^{6} (3 x) d x

\int 2 3 x - 1 d x

5 \frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 9 x = 2 cos (3 t)

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