∫dx/x(x^7+2)
=∫x^6dx/[x^7(x^7+2)]
=(1/7)∫d(x^7)/[x^7(x^7+2)]
=(1/14)∫[(1/x^7)-[1/(x^7+2)]]d(x^7)
=(1/14)[ln(x^7)-ln(x^7+2)]+c
=(1/14)ln[(x^7)/(x^7+2)]+c
∫dx/x(x^7+2)
=∫x^6dx/[x^7(x^7+2)]
=(1/7)∫d(x^7)/[x^7(x^7+2)]
=(1/14)∫[(1/x^7)-[1/(x^7+2)]]d(x^7)
=(1/14)[ln(x^7)-ln(x^7+2)]+c
=(1/14)ln[(x^7)/(x^7+2)]+c