Integrate x2n-1 sin xn dx.

x2n-1sinxndx=xn×xn-1sinxndx=1nxn×nxn-1sinxndx   multiplying and dividing by nNow let xn=t such that nxn-1dx=dt1nxn×nxn-1sinxndx=1ntsint dt=1ntsintdt-ddttsintdtdt=1n-tcost--costdt=1n-tcost+costdt=1n-tcost+sint+CNow substituiting we get, =1n-xncosxn+sinxn+C  Answer.

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