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

[Tidus810]

Re: I need help with calculus homework

Preeetty sure everything you did there was correct, haha.
1 - no integral sign, that's all.
2 - is it 8^t2/3 or 8(t^2/3)? If it's the second, then the solved integral is just 8(3/5)t^5/3, or 24t^5/3 all over 5.
3 - correct.

Hope that helps, even though you don't look like ya needed it. :P

[Reincarnate]

Re: I need help with calculus homework

1. Without
2. Assuming you ask for the integral of 8(t^2/3), it'd be like 8 * the integral of t^2/3. Increasing the exponent here by 1 is the same as increasing it by 3/3, so (t^(5/3))/(5/3). Multiply by the 8 you moved out and you get (24/5)t^(5/3) + C
3. The integral of 1/x dx is ln(x)+C. So the integral of 9/u du is simply 9*ln(u) + C


EDIT: Watch out Tidus -- you divide by the raised exponent, not multiply

[Organist]

Re: I need help with calculus homework

perfect thanks guys