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$Evaluate \int \frac{1}{x^{2} \sqrt{1 + x^{2}}} d x$

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−x2+1x+c

−xx2+1+c

−x2-1x+c

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detailed solution

Correct option is A

Let x = tanθ or dx = sec2θ dθ ∴ ∫1x21+x2dx=∫sec2⁡θdθtan2⁡θsec⁡θ =∫cosec⁡θcot⁡θdθ =−cosec⁡θ+c =−x2+1x+c

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Evaluate ∫1x21+x2dx

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$Evaluate \int \frac{1}{x^{2} \sqrt{1 + x^{2}}} d x$