Question

Can anyone help me integrate this manually?

sqrt(h)/(0.1-sqrt(h))

I have a feeling you have to use polynomial long division, but I don't get the same answer as a calculator. If anyone can shed any light that would be awesome.

Answer 1

www.wolframalpha.com/input/?i=integal+of+sqrt(h)%2F(0.1-sqrt(h))

Answer 2

You can substitute \[u=\sqrt{h}\]

Answer 3

Please continue, I have done this already

Answer 4

Show us what youv'e got. And let us verify.

Answer 5

Can you pls just do it for me?

Answer 6

What is du, then?

Answer 7

dh=du2sqrt(h) or du/dh=1/2sqrt(h)

Answer 8

Please just do this question for me, haha

Answer 9

I will understand when I see the process.

Answer 10

Okay. So\[dh = 2\sqrt{h} du\]
Upon substitution, we'll get
\[2\int\limits_{}^{}\frac{ u^2 }{ 0.1-u }du\]
Then perform the long division. I think you can do this right?

Answer 11

Okay, I think after long division I should get....

Can you confirm?

integral -u-0.1+(0.01/-u+0.1).du

Answer 12

Correct!
But you can actually rewrite this like
2\[2\int\limits_{}^{}(-u- \frac{0.01 }{ u-0.1 }-0.1) du\]
Just integrate them separately. :D

Answer 13

Thank you so much. Awesome.

Answer 14

Easy, right?! haha. :)

Answer 15

Uhm, not really. I'm just going with it, haha.

Answer 16

Just continue where you are. :)

Answer 17

Oh, I can integrate the polynomial, haha. Long division and the substitutiuon was hard

Answer 18

Yeah. As what I've told you. :)