Question

integral of 1/((x+5)(sqrt(x^2+5x)))

Answer 1

\[\int\limits_{}^{}\frac{1}{((x+5)(\sqrt{x^{2}+5}))}\]
here this is a bit easier to see.

Answer 2

\[\int\limits_{}^{}\frac{(x^{2}+5)^{-1/2}}{x+5}\]
another way to write it.

Answer 3

substitution? maybe?
\[u=x^{2}+5\]
\[du=2xdx\]
\[\frac{du}{2x}=dx\]

Answer 4

\[\int\limits_{}^{}\frac{(u)^{-1/2}}{x+5}\]

Answer 5

I have to get going or else I'd stay and try to help. I would recommend this http://www.wolframalpha.com/input/?i=intigral+of+1%2F%28%28x%2B5%29%28sqrt%28x^2%2B5x%29%29%29 for you to check your work.

Answer 6

@Kkutie7, it is x^2+5x, you are missing a x

Answer 7

try this substitution
\[x+5 = 5 \sec^2 u\]
\[dx = 10 \sec^2 u \tan u du\]
\[\rightarrow \int\limits \frac{10 \sec^2 u \tan u}{(5 \sec^2 u) \sqrt{5 \sec^2 u} \sqrt{5\sec^2 u - 5}} du\]
\[ = \frac{2}{5} \int\limits \cos u du\]
\[= \frac{2}{5} \sin u +C\]
From substitution we know that
\[\cos^2 u = \frac{5}{x+5}\]
\[\rightarrow \sin^2 u = 1- \frac{5}{x+5} = \frac{x}{x+5}\]
final answer:
\[\rightarrow \frac{2}{5} \sqrt{\frac{x}{x+5}} +C\]

Answer 8

best response of the day!@dumbcow

Answer 9

sorry for the complex substitution, i was trying to save steps
you can get same result by doing

w^2 = x+5
2w dw = dx

then do
w = sqrt5 sec u
dw = sqrt5 sec u tan u

Answer 10

@caozeyuan , well thank you :)