∫$$dx(x+2)x2+4x+8$$ is equal to

Correct option is 1−12log⁡1(x+2)+1(x+2)2+14+C

Questions

$\int \frac{dx}{(x + 2) \sqrt{x^{2} + 4 x + 8}}$ is equal to

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−12log⁡1(x+2)+1(x+2)2+14+C

−log⁡1(x+2)+1(x+2)2+14+C

12log⁡1(x+2)+1(x+2)2+14+C

None of the above

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detailed solution

Correct option is A

Put x+2=1t⇒dx=−dtt2 Now x2+4x+8=(x+2)2+4So=∫−dtt21t1t2+4=−∫dt1+4t2=−12∫dtt2+14=−12ln⁡t+t2+14+C=−12ln⁡1x+2+1(x+2)2+14+C

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∫dx(x+2)x2+4x+8 is equal to

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$\int \frac{dx}{(x + 2) \sqrt{x^{2} + 4 x + 8}}$ is equal to