Finding the area of sectors of an ellipse

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How do I integrate the following polar integral? I'm not sure if it is possible. $$ 0.5 \int\left( \frac{17.737 (1 - 0.967^2) }{1+0.967 \cos \theta}\right)^2 d \theta $$ or the general case: $$ 0.5 \int\left( \frac{a (1 - e^2) }{1+e \cos \theta}\right)^2 d \theta $$ Where $0<e<1$.