If f(x)=log⁡xx3, then its antiderivative F(x)given by

F(x)=∫log⁡xx3dx=log⁡x∫1x3dx−∫1x∫1x3dxdx =−12x2log⁡x+12∫1x3dx+ Constant =−12x2log⁡x−14x2+C=−12x2log⁡x+12log⁡e+C=−12x2log⁡xe+C