Question

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

∫(x+2)/(x²+2) dx

Thank you!!

Answer 1

If x = √2 tan t,

x² = 2tan²t
x² + 2 = 2sec²t
dx = √2 sec²t

and the integrand becomes

(√2 tan t + 2)/(2sec²t) * √2 sec²t
= (√2 tan t + 2)/√2 = tan t + √2

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