Question

int 1/ [x^-1/2 (x + 2]

Answer 1

\[\int\limits 1 / [\sqrt[]{x} (x+2)]\]

Answer 2

\[\int\limits_{}^{}\frac{1}{\sqrt{x}(x+2)}dx=\int\limits_{}^{}\frac{1}{2\sqrt{x}(1+\frac{x}{2})}dx=\int\limits_{}^{}\frac{1}{2\sqrt{x}(1+(\frac{\sqrt{x}}{\sqrt{2}})^{2})}dx\]\[(-\sqrt{2})\int\limits_{}^{}\frac{1}{(-\sqrt{2})2\sqrt{x}(1+(\frac{\sqrt{x}}{\sqrt{2}})^{2})}dx\]\[(-\sqrt{2})\tan^{-1} (\frac{\sqrt{x}}{\sqrt{2}})\]

Answer 3

thx dude

Answer 4

remember this:
\[\int\limits_{}^{}\frac{f \prime}{1+f ^{2}}dx=\tan^{-1} (f)\]

Answer 5

k