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

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

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integral of 2cos(y^2)

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

2 π C (\frac{2}{π} y) + C

Solution steps

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

Use the nonelementary integral:

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

= 2 \frac{π}{2} C (\frac{2}{π} y)

Simplify

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

= 2 π C (\frac{2}{π} y)

Add a constant to the solution

= 2 π C (\frac{2}{π} y) + C

e^{x + y} d x + e^{x - y} d y = 0

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f (x) = \frac{3 x ^{2}}{ln ( x )}

\int \frac{x ^{3}}{( 6 - x ^{4} ) ^{2}} d x

\int \frac{7 x ^{2} + 16 x - 19}{x ^{2} + 2 x - 3} d x

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