Answer
$\frac 1{4\pi}sin2\pi x^2+C$
Work Step by Step
$\int x(cos2\pi x^2)$
$u=2\pi x^2; du=4\pi xdx$
$\frac 1{4\pi} \int (cos2\pi x^2)(4\pi x)dx$
$\frac 1{4\pi}sin2\pi x^2+C$
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