∫dxx(x7+1)  is equal to

∫dxx(x7+1)  which is of the form 1xf(xn) =∫x6x7(x7+1)dx,  substitute x7=t ⇒7x6dx=dt =∫17dtt(t+1) =17∫(1t+−1t+1)dt =17log|tt+1|+C =17log(x7x7+1)+C  assuming thatx>0