∫$$dxx2+2x+2$$ is equal to

Correct option is 1log∣(x+1)+x2+2x+2∣+C

Questions

$\int \frac{dx}{\sqrt{x^{2} + 2 x + 2}}$ is equal to

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log∣(x+1)+x2+2x+2∣+C

log∣x+x2+2x+2∣+C

log⁡x+1−x2+2x+2+C

None of the above

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detailed solution

Correct option is A

Let =∫dxx2+2x+2=∫dxx2+2x+1+1=∫1(x+1)2+(1)2dx (let x+1=t)⇒dx=dt∴ I=∫dtt2+1=log⁡t+t2+1+C ∵∫dxx2+a2=log⁡x+x2+a2=log⁡(x+1)+(x+1)2+1+C=log⁡(x+1)+x2+2x+2+C

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∫dxx2+2x+2 is equal to

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$\int \frac{dx}{\sqrt{x^{2} + 2 x + 2}}$ is equal to