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$\int \frac{d x}{a^{2} \cos^{2} x + b^{2} \sin^{2} x} (a, b > 0)$ is equal to

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sin−1⁡((a/b)tan⁡x)+C

tan−1⁡((b/a)tan⁡x)+C

1abtan−1⁡batan⁡x+C

none of these

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detailed solution

Correct option is C

Putting t=tan⁡x we get∫dxa2cos2⁡x+b2sin2⁡x=∫sec2⁡xdxa2+b2tan2⁡x=∫dta2+b2t2=1b2∫dtt2+a2/b2=1b2⋅batan−1⁡bat+C=1abtan−1⁡batan⁡x+C.

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∫dxa2cos2⁡x+b2sin2⁡x(a,b>0) is equal to

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$\int \frac{d x}{a^{2} \cos^{2} x + b^{2} \sin^{2} x} (a, b > 0)$ is equal to