Is this your integral?
∫9(3x+10)6dx
If so....
Let's pick u = 3x + 10 which means du = 3 dx and then substitute these in like this:
=∫9(3x+10)6dx =∫3⋅3(3x+10)6dx =3∫(3x+10)6⋅3dx =3∫u6⋅du =3∫u6du
Now we can use the rule which says ∫undu = un+1n+1+c to get...
=3⋅u77+c =37u7+c
Now let's substitute 3x + 10 back in for u
=37(3x+10)7+c