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Integrate the following and please simplify it. 1 / (a^2sin^2x + b^2cos^2x)

Integrate the following and please simplify it. 1 / (a^2sin^2x + b^2cos^2x)

Grade:12

1 Answers

Arun
25763 Points
3 years ago
∫ 1/(a²cos²x + b²sin²x) dx

= ∫ sec²x/(a² + b²tan²x) dx [dividing up and down by cos²x] 

put btanx = u and sec²x dx = du/b. the integral becomes 

(1/b) ∫ du/(a² + u²) 

= (1/b) [(1/a) tanֿ¹(u/a)] 

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