Question

use u-substituion rule to find the anti derivative of
(1/cos^2(6x)) dx

Answer 1

sec to 2 power (6x)

Answer 2

\[\int\limits_{}^{} \frac {dx}{\cos^2 (6x)} = \int\limits_{}^{} \sec^2 (6x) dx\]\[u = 6x, \frac {1}{6}du = dx\]\[\int\limits\limits_{}^{} \sec^2 (6x) dx = \frac {1}{6} \int\limits\limits_{}^{} \sec^2 u du = \frac {1}{6} \tan u + C = \frac {1}{6} \tan (6x) + C\]

Answer 3

1/cos^2x = sec^2x
=int sec^2(6x)dx
Let u = 6x --> du/6 = dx
= (1/6) Int sec^2udu = (1/6)tan(6x) + C