You need to evaluate the indefinite integral by performing the substitution `x^2 = t` , such that:
`x^2 = t => 2xdx = dt => xdx = (dt)/2`
`int x*sin(x^2) dx= (1/2)int sin t dt`
`(1/2)int sin t dt= (1/2)(-cos t) + c`
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Replacing back `x^2` for t yields:
`int x*sin(x^2) dx= -(1/2)(cos x^2) + c`
Hence, evaluating the indefinite integral yields `int x*sin(x^2) dx= -(1/2)(cos x^2) + c`
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