dx-2-4-

Question Number 86034 by ar247 last updated on 26/Mar/20

\int \frac{d x}{\sqrt{\times^{2} + 4}}

Answered by TANMAY PANACEA. last updated on 26/Mar/20

x = 2 t a n a \frac{d x}{d a} = 2 {s e c}^{2} a

\int \frac{2 {s e c}^{2} a d a}{2 s e c a}

\int s e c a d a = l n (s e c a + t a n a) + c

l n (\frac{x}{2} + \sqrt{1 + \frac{x^{2}}{4}}) + c

l n (x + \sqrt{x^{2} + 4}) - l n 2 + c

l n (x + \sqrt{x^{2} + 4}) + C

Answered by Rio Michael last updated on 26/Mar/20

\int \frac{d x}{\sqrt{x^{2} + 4}} = arsinh (\frac{x}{2}) + k