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$\int \frac{l o g (x + \sqrt{1 + x^{2}})}{\sqrt{1 + x^{2}}} d x$

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12log(x+1+x2)2+c

log(x+1+x2)2+c

log(x+1+x2)+c

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detailed solution

Correct option is A

Let logx+1+x2 =tDifferentiating, we get1x+1+x21+2x21+x2dx=dt⇒11+x2dx=dt∴∫logx+1+x21+x2dx=∫t dt =t22+c =12logx+1+x22+c

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∫log(x+1+x2)1+x2dx

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$\int \frac{l o g (x + \sqrt{1 + x^{2}})}{\sqrt{1 + x^{2}}} d x$