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

The integral of 2ye^{y^2} is e^{y^2}+C

Popular >

integral of 2ye^{y^2}

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

e^{y^{2}} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

= 2 \cdot \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

= 2 \cdot \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= 2 \cdot \frac{1}{2} e^{u}

Substitute back

u = y^{2}

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

Simplify

2 \cdot \frac{1}{2} e^{y^{2}} : e^{y^{2}}

= e^{y^{2}}

Add a constant to the solution

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

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

\frac{d y}{d x} + y \cdot 1 + x^{2} = 0

\frac{d y}{d x} = \frac{x}{( 1 + 2 y )}, y (- 1) = 0

f (x) = 9 + 5 x^{2} - 2 x^{3}, at x = a

\int \frac{1}{9 - 36 x ^{2}} d x