∫$$ex11+x2+1$$−$$2x21+x25dx$$

Correct option is 1ex11+x2+x1+x23+C

Questions

$\int e^{x} [\frac{1}{\sqrt{1 + x^{2}}} + \frac{1 - 2 x^{2}}{\sqrt{{(1 + x^{2})}^{5}}}] dx$

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detailed solution

Correct option is A

I=∫ex11+x2−x1+x23+x1+x23+1−2x21+x25dxI=ex11+x2+exx1+x23+CI=ex11+x2+x1+x23+C∵ using ∫exf(x)+f′(x)dx=exf(x)+C

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∫ex11+x2+1−2x21+x25dx

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$\int e^{x} [\frac{1}{\sqrt{1 + x^{2}}} + \frac{1 - 2 x^{2}}{\sqrt{{(1 + x^{2})}^{5}}}] dx$