Question

Use either substitution or integration by parts to evaluate the integral:

∫(x+2)/(x²+2) dx

Thank you!!
If x = √2 tan t,
x<sup>2</sup> = 2tan<sup>2</sup>t
x<sup>2</sup> + 2 = 2sec<sup>2</sup>t
dx = √2 sec<sup>2</sup>t

and the integrand becomes

(√2 tan t + 2)/(2sec<sup>2</sup>t) * √2 sec<sup>2</sup>t
= (√2 tan t + 2)/√2 = tan t + √2

Play around with that, remembering that d(cost) = -sint

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