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Question Number 57817 by Abdo msup. last updated on 12/Apr/19

f i n d t h e v a l u e o f \int_{\frac{π}{3}}^{\frac{π}{2}} \frac{d x}{\sqrt{2 {c o s}^{2} x + 3 {s i n}^{2} x}}

Commented by mr W last updated on 13/Apr/19

Incomplete elliptic integral of the first kind, no elementary solution.

Answered by tanmay.chaudhury50@gmail.com last updated on 13/Apr/19

2 {c o s}^{2} x + 3 {s i n}^{2} x

= 2 + {s i n}^{2} x

= 2 + \frac{1 - c o s 2 x}{2}

= \frac{5 - c o s 2 x}{2}

\int_{\frac{π}{3}}^{\frac{π}{2}} \frac{\sqrt{2} d x}{\sqrt{5 - c o s 2 x}}

n o w \dots \int \frac{d x}{\sqrt{a + b c o s x}} f o r m a t \dots w a i t \dots