let f(x)=∫_0 ^(2π) ((sin(2t))/(1+x cos(t)))dt 1) find a explicit form of f(x) 2) find also g(x)=∫_0 ^(2π) ((sin(2t)cost)/((1+xcost)^2 ))dt 3)find the value of ∫_0 ^(2π) ((sin(2t))/(1+3 cos(t)))dt and ∫_0 ^(2π) ((cost sin(2t))/((1+3cost)^2 ))dt .


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Question Number 48264 by Abdo msup. last updated on 21/Nov/18

$l e t f (x) = \int_{0}^{2 π} \frac{s i n (2 t)}{1 + x c o s (t)} d t$ $1) f i n d a e x p l i c i t f o r m o f f (x)$ $2) f i n d a l s o g (x) = \int_{0}^{2 π} \frac{s i n (2 t) c o s t}{{(1 + x c o s t)}^{2}} d t$ $3) f i n d t h e v a l u e o f \int_{0}^{2 π} \frac{s i n (2 t)}{1 + 3 c o s (t)} d t a n d$ $\int_{0}^{2 π} \frac{c o s t s i n (2 t)}{{(1 + 3 c o s t)}^{2}} d t .$
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