Question

Stupid question: I programmed a numerical method that can integrate this, but can it be solved analytically?
\[L=\int_{0}^{18}\sqrt{1+\frac{1}{2x}+\frac{x}{2}}dx\]

Answer 1

I'm too stupid for this question :)

Answer 2

ikr. metoo xD

Answer 3

O_O

Answer 4

Last time I worked with integrals was > 20 years ago.
I used to like drawing that elongated s shape :) :) memories :)

Answer 5

Nevermind: It can be solved analytically.

Answer 6

Integration is on my list to refresh myself on - but I suspect I won't try this one at first (since you posted it) :)

Answer 7

It's not that bad; you just have to do some tricky algebra.

Here are some the steps (if you ever want to give it a try):
\[L=\int\sqrt{1+\frac{1}{2x}+\frac{x}{2}}dx\]\[L=\int\sqrt{\frac{2x}{2x}+\frac{1}{2x}+\frac{x^2}{2x}}dx\]\[L=\int\sqrt{\frac{(x+1)^2}{2x}}dx\]\[L=\int\frac{x+1}{\sqrt{2x}}dx\]\[L=\int\frac{x}{\sqrt{2x}}dx+\int\frac{1}{\sqrt{2x}}dx\]\[L=\frac{1}{3}\sqrt{2}x^{3/2}+\sqrt{2x}+C\]

Answer 8

yes

Answer 9

sir help me please it's my home work (x2+2x+3)(x2+4x+3)>0

Answer 10

How in the world did you find this month-old thread? xd