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

The integral of ycos(x^2) is ysqrt(pi/2)\C(sqrt(2/pi)x)+C

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integral of ycos(x^2)

\int y cos (x^{2}) d x

y \frac{π}{2} C (\frac{2}{π} x) + C

Solution steps

\int y cos (x^{2}) d x

Take the constant out:

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

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

Use the nonelementary integral:

\int cos (x^{2}) d x = \frac{π}{2} C (\frac{2}{π} x)

= y \frac{π}{2} C (\frac{2}{π} x)

Add a constant to the solution

= y \frac{π}{2} C (\frac{2}{π} x) + C

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