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

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

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integral of 2sin(x^2)

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

2 π § (\frac{2}{π} x) + C

Solution steps

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

Take the constant out:

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

= 2 \cdot \int sin (x^{2}) d x

Use the nonelementary integral:

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

= 2 \frac{π}{2} § (\frac{2}{π} x)

Simplify

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

= 2 π § (\frac{2}{π} x)

Add a constant to the solution

= 2 π § (\frac{2}{π} x) + C

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