Question

Integrate the function: $x sin \ x$

Answer 1

Let\ I=$$∫x sin\ x dx

Taking x as first function and $sin \ x$ as second function and integrating by parts, we obtain

$I =$ $x∫sin\ x dx-∫[{(\frac {d}{dx} x)∫sin\ x dx}]dx$

I =$$x(-cosx)-∫1.(-cosx)dx

$I =-xcos\ x+sin\ x+C$