What is the integral of 2sin(y^2) ?

The integral of 2sin(y^2) is sqrt(2)sqrt(pi)\S(sqrt(2/pi)y)+C

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integral of 2sin(y^2)

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

2 π § (\frac{2}{π} y) + C

Solution steps

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

Use the nonelementary integral:

\int sin (x^{2}) d x = \frac{π}{2} § (\frac{2}{π} x)

= 2 \frac{π}{2} § (\frac{2}{π} y)

Simplify

2 \frac{π}{2} § (\frac{2}{π} y) : 2 π § (\frac{2}{π} y)

= 2 π § (\frac{2}{π} y)

Add a constant to the solution

= 2 π § (\frac{2}{π} y) + C

y = 4 x

\frac{S + \frac{1}{2}}{S ^{2} - 2 S + 5}

\frac{\partial}{\partial x} (e^{x} sin (10 y + 5 z))

\frac{d}{d x} (2 arcsin (x^{2}))

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

What is the integral of 2sin(y^2) ?
The integral of 2sin(y^2) is sqrt(2)sqrt(pi)\S(sqrt(2/pi)y)+C