What is the integral of 4cos(x^2) ?

The integral of 4cos(x^2) is 2sqrt(2)sqrt(pi)\C(sqrt(2/pi)x)+C

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integral of 4cos(x^2)

\int 4 cos (x^{2}) d x

22 π C (\frac{2}{π} x) + C

Solution steps

\int 4 cos (x^{2}) d x

Take the constant out:

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

= 4 \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)

= 4 \frac{π}{2} C (\frac{2}{π} x)

Simplify

4 \frac{π}{2} C (\frac{2}{π} x) : 22 π C (\frac{2}{π} x)

= 22 π C (\frac{2}{π} x)

Add a constant to the solution

= 22 π C (\frac{2}{π} x) + C

(tan (x) - sin (x) sin (y)) d x + cos (x) cos (y) d y = 0

x y^{^{'}} - x - x^{2} - 3 y = 0

\int \frac{3 t ^{2}}{t ^{3} + 5} d t

\int x \cdot x + 3 d x

\frac{\partial}{\partial y} (x + y sin (t))

What is the integral of 4cos(x^2) ?
The integral of 4cos(x^2) is 2sqrt(2)sqrt(pi)\C(sqrt(2/pi)x)+C