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

The integral of cos^2(x^2) is 1/2 (x+(sqrt(pi))/2 \C((2x)/(sqrt(pi))))+C

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integral of cos^2(x^2)

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

\frac{1}{2} (x + \frac{π}{2} C (\frac{2 x}{π})) + C

Solution steps

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

Rewrite using trig identities

= \int \frac{1 + cos ( 2 x ^{2} )}{2} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int 1 + cos (2 x^{2}) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int 1 d x + \int cos (2 x^{2}) d x)

\int 1 d x = x

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

= \frac{1}{2} (x + \frac{π}{2} C (\frac{2 x}{π}))

Add a constant to the solution

= \frac{1}{2} (x + \frac{π}{2} C (\frac{2 x}{π})) + C

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What is the integral of cos^2(x^2) ?
The integral of cos^2(x^2) is 1/2 (x+(sqrt(pi))/2 \C((2x)/(sqrt(pi))))+C