So (1) becomes:
You can check the answer here to make sure.
int (0.8(3 + 2 ln(u))^3)/u - Wolfram|Alpha
Could you explain where I went wrong with this one?
(int) 0.8((3 + 2 ln(u))^3) du/u
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.
So plugging in and we get:
You can check the answer by taking the derivative of which
is equal to
derivative 0.8((3 + 2 ln(u))^4}/8) + C - Wolfram|Alpha
Hope it answers your question.
So by integrating what you'll get is when differentiated will be what you're integrating.
you're integrating and you'll get
When you differentiate you'll get what you're integrating. So when you integrate you've to rearrange variables and constants in such a way that when you differentiate the rearrangement you'll end up with what you're integrating.
So if we differentiate we get:
Let which is what you're integrating.
And that's why