Evaluate ∫$$sec2$$⁡$$xtan2$$⁡$$x+4dx$$

Correct option is 1log⁡tan⁡x+tan2⁡x+4+C

Questions

$Evaluate \int \frac{\sec^{2} x}{\sqrt{\tan^{2} x + 4}} d x$

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log⁡tan⁡x+tan2⁡x+4+C

14log⁡tan⁡x+tan2⁡x+4+C

log⁡tan⁡x+tan2⁡x+2+C

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detailed solution

Correct option is A

Since derivative of tan x is sec2xLet tan x = t or sec2x dx = dt∴ ∫sec2⁡xtan2⁡x+4dx=∫dtt2+22=log⁡t+t2+4+C=log⁡tan⁡x+tan2⁡x+4+C

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Evaluate ∫sec2⁡xtan2⁡x+4dx

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$Evaluate \int \frac{\sec^{2} x}{\sqrt{\tan^{2} x + 4}} d x$