I-think-it-will-be-0-pi-4-dx-1-tanx-0-pi-4-dx-1-x-4-1-2-1-2-4-2-1-3-2-4-1-3-4-3-1-3-5-2-4-6-1-4-4-4-

Question Number 86365 by Prithwish Sen 1 last updated on 28/Mar/20

I think it will be

\int_{0}^{\frac{π}{4}} \frac{dx}{\sqrt{1 + tanx}} \approx \int_{0}^{\frac{π}{4}} \frac{dx}{\sqrt{1 + x}}

= \frac{π}{4} - \frac{1}{2} . \frac{1}{2} . {(\frac{π}{4})}^{2} + \frac{1.3}{2.4} . \frac{1}{3} . {(\frac{π}{4})}^{3} - \frac{1.3.5}{2.4.6} . \frac{1}{4} {(\frac{π}{4})}^{4} + \dots .