∫1/(2-(sinx)^2)dx如何积分?

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∫1/(2-(sinx)^2)dx如何积分?
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∫1/(2-(sinx)^2)dx如何积分?
∫1/(2-(sinx)^2)dx如何积分?

∫1/(2-(sinx)^2)dx如何积分?
∫1/(2-sin^2 x)dx
=∫1/(2cos^2 x + sin^2x)dx
=∫1/(2 + tan^2 x) (1/cos^2 xdx)
=∫1/(2 + tan^2 x) dtanx
=1/√2∫1/(1 + (tanx/√2)^2) d(tanx/√2)
=1/√2 arctan(tanx/√2) + C