What is the integral of (1-cos(2x^2))/(x^2) ?

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

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integral of (1-cos(2x^2))/(x^2)

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

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

Solution steps

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

Apply Integration By Parts

: - \frac{1 - cos ( 2 x ^{2} )}{x} - \int - 4 sin (2 x^{2}) d x

= - \frac{1 - cos ( 2 x ^{2} )}{x} - \int - 4 sin (2 x^{2}) d x

\int - 4 sin (2 x^{2}) d x = - 2 π § (\frac{2}{π} \frac{2 x}{2})

= - \frac{1 - cos ( 2 x ^{2} )}{x} - (- 2 π § (\frac{2}{π} \frac{2 x}{2}))

Simplify

= - \frac{1 - cos ( 2 x ^{2} )}{x} + 2 π § (\frac{2}{π} \frac{2 x}{2})

Add a constant to the solution

= - \frac{1 - cos ( 2 x ^{2} )}{x} + 2 π § (\frac{2}{π} \frac{2 x}{2}) + C

y = tan^{3} (x)

\frac{d}{d x} (\frac{- x}{16 - x ^{2}})

\frac{1}{s ^{2} + 4 s + 4}

\frac{\partial}{\partial x} ((x^{- 2} + y^{- 2})^{3})

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