- #1

- 169

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This is my attempt:

##x = \sqrt{3} \tan \theta## --> ##dx = \sqrt{3} \sec^2 \theta \ d\theta##

##x^2 + 3 = (\sqrt{3} \tan \theta)^2 + 3##

##= 3 \tan^2 \theta + 3##

##= 3 (\tan^2 \theta + 1)##

##= 3 \sec^2\theta##

##\int \frac{1}{x^2 + 3} \ dx = \int \frac{1}{3 \sec^2\theta} (\sqrt{3} \sec^2 \theta \ d\theta)##

##= \frac{\sqrt{3}}{3} \int d\theta##

##= \frac{\sqrt{3}}{3} \theta + C##

Is there any next steps?

Is this correct?

Thanks