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Integrate: sinx cosx/a^2 cos^2x+b^2 sin^2x

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Solution: Here,

$I=int sinxcdot cosx/a^2cos^2x+b^2sin^2xhspace0.1cmdx$

Put , $a^2cos^2x+b^2sin^2x=tRightarrow [a^2(-2cosxcdot sinx)+b^2(2sinxcdot cosx)]dx=dt$

$\ I=int dt/2(b^2-a^2)t=1/2(b^2-a^2)hspace0.1cmlog left | t ight |+c\ \Rightarrow I=1/2(b^2-a^2)hspace0.1cmlog left | a^2cos^2x+b^2sin^2x ight |+c$

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Deependra Verma

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