1.

Solve ∫ sec2 x cosec2 x dx on I ⊂ R [{nπ : n ∈ Z} ∪ {(2n + 1) (π/2) : n ∈ Z}]

Answer»

∫ sec2 x.cosec2 x dx 

= ∫ (1/(cos2 x sin2 x)) dx

= ∫ (sin2 x + cos2 x/(cos2 x.sin2 x)) dx

= ∫ (1/cos2 x) dx + ∫ (1/sin2 x) dx 

= ∫ sec2 x dx + ∫ cosec2 x dx 

= tan x – cot x + C



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