I need help with calculus homework

[Organist]

I have just a couple questions regarding integrals

first question:

if I'm taking the integral of something like:

∫x^5dx would it equal x^6/6+c without the integral sign? or is the integral sign included

second question: I need help finding the integral of functions that include fractional exponents like:

∫8^t 2/3 dt

= 8∫t^2/3dt
= (8^t5/3)/5/3 +c (because I added one to the exponent)

but I get stuck here.. what do I do after this? multiply by it's recipriol? I'm not sure how to do that

Last question:

is it true that:

∫1/xdx = natural log of the absolute value of x plus your constant?

I want to make sure I did this problem correctly:

∫9/u du
= 9∫1/u du
= 9ln lul + c?

or is this wrong?

thx