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

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

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integral of sin^2(x^2)

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

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

Solution steps

\int sin^{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

x \to - 4 - lim (\frac{2 - x}{4 - x})

x + \frac{4}{x}

\int - 3 cos (4 x) d x

\int_{1}^{2} x e^{8 x^{2}} d x

x y^{^{'}} + 2 y = - e^{x}

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