Integration: General Power Formula

Could you explain where I went wrong with this one?

**28-1-16**

(int) 0.8((3 + 2 ln(u))^3) du/u

Attempt:

u = 3 + 2 ln u

du = 1 / u

Therefore answer should be:

(.8 [3 + 2 ln u]^3) / 4

the ti-89 comes up with another answer when this integration is performed, which is long and bizarre.

Re: Integration: General Power Formula

Let

So (1) becomes:

You can check the answer here to make sure.

int (0.8(3 + 2 ln(u))^3)/u - Wolfram|Alpha

Re: Integration: General Power Formula

Re: Integration: General Power Formula

Hi how did 0.8m^3 / 2 turn into 0.8m^4 / 8?

how did the division by 2 turn into a division by 8?

Re: Integration: General Power Formula

Surely you know that ...

Re: Integration: General Power Formula

Re: Integration: General Power Formula

Quote:

Originally Posted by

**Prove It** Surely you know that

...

what confuses me is according to the general power rule, you add 1 to the exponent found on the integral, which is 3, so ends up being 4 on the bottom. While I understand it differentiates properly (post #6), seems like something other than general power rule was used to come up with a denominator of 8.

Re: Integration: General Power Formula

Quote:

Originally Posted by

**togo** what confuses me is according to the general power rule, you add 1 to the exponent found on the integral, which is 3, so ends up being 4 on the bottom. While I understand it differentiates properly (post #6), seems like something other than general power rule was used to come up with a denominator of 8.

You first separate the constants from variable. So it will be: