The integral of f(x)=3xcos⁡x is given by

I=∫3xcos⁡xdx =3xsin⁡x−log⁡3∫3xsin⁡xdx =3xsin⁡x−log⁡3−3xcos⁡x+(log⁡3)∫3x                                                             cos x dx]     =3xsin⁡x+(log⁡3),3xcos⁡x−(log⁡3)2⇒      1+(log⁡3)2I=3x(sin⁡x+(log⁡3)cos⁡x)I=3x(sin⁡x+(log⁡3)cos⁡x)1+(log⁡3)2