Integral of $$sec2$$⁡$$xdx3tan2$$⁡$$x+5sec2$$⁡$$x+1dx$$ is equal to

Correct option is 1143tan−12r3+k

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$Integral of \frac{\sec^{2} x d x}{3 \tan^{2} x + 5 \sec^{2} x + 1} d x is equal to$

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143tan−12r3+k

14tan−12r3+c

13tan−12r3+k

14tan−12r3+c

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detailed solution

Correct option is A

∫sec2xdx3tan2x+5sec2x+1=∫sec2xdx3tan2x+51+tan2x+1tan⁡x=rsec2⁡xdx=dr=∫dr3r2+5r2+6=∫dr8r2+6=18∫drr2+68=18∫drr2+322 Use formula I=∫1r2+a2dr=1atan−1⁡ra+k=18132tan−1⁡r32+k=143tan−1⁡2r3+k

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Integral of sec2⁡xdx3tan2⁡x+5sec2⁡x+1dx is equal to

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$Integral of \frac{\sec^{2} x d x}{3 \tan^{2} x + 5 \sec^{2} x + 1} d x is equal to$