Question

CAN I GET HELP FROM AN INTEGRAL PROBLEM

Answer 1

\[\int\limits_{}^{}\frac{ \sqrt{x+5} }{ x }\]

Answer 2

Let u = numerator. do some steps. show me your work, please

Answer 3

I don't know how to approach this problem

Answer 4

Let \(u=\sqrt{x+5}\) then \(du =\dfrac{1}{2\sqrt{x+5}}dx\) moreover \(u^2= x+5 ~~or~~x= u^2-5\)

Answer 5

from du, you can see that \(2\sqrt{x+5} du=dx\) replace again, you get \(2udu =dx\) ok?

Answer 6

I got \[\int\limits_{}^{}2+\frac{ 10 }{ u^2 -5}\]

Answer 7

From Mathematica 9:\[\int\limits \frac{\sqrt{x+5}}{x} \, dx=2 \sqrt{x+5}-2 \sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{x+5}}{\sqrt{5}}\right) \]