求∫dx/(a^2sin^2x+b^2cos^2x)解答

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求∫dx/(a^2sin^2x+b^2cos^2x)解答
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求∫dx/(a^2sin^2x+b^2cos^2x)解答
求∫dx/(a^2sin^2x+b^2cos^2x)解答

求∫dx/(a^2sin^2x+b^2cos^2x)解答
∫dx/(a^2sin^2x+b^2cos^2x)
=∫dx/a^2*cos^2x*(tan^2x+b^2/a^2)
=1/a^2∫sec^2xdx/(tan^2x+b^2/a^2)
=1/a^2∫d(tanx)/(tan^2x+(b/a)^2)
=1/a^2*a/b*arctan(ax/b)+C
=(1/ab)*arctan(ax/b)+C

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