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
Use either substitution or integration by parts to evaluate the integral:
∫(x+2)/(x²+2) dx
Thank you!!
1 answer