Evaluate ∫$$2xx2+1x2+2dx$$

Correct option is 1log⁡x2+1−log⁡x2+2+C

Questions

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

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log⁡x2+1−log⁡x2+2+C

log⁡x2+2−log⁡x2+1+C

log⁡x2+1+log⁡x2+2+C

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detailed solution

Correct option is A

Let I=∫2xx2+1x2+2dx Putting x2=t and 2xdx=dt, we get I=∫dt(t+1)(t+2)=∫1t+1−1t+2dt=log⁡|t+1|−log⁡|t+2|+C=log⁡x2+1−log⁡x2+2+C

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Evaluate ∫2xx2+1x2+2dx

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