不定积分：

常用技巧：乘以 $\frac{\sec\theta+\tan\theta}{\sec\theta+\tan\theta}$：

$$\int\sec\theta\,d\theta =\int\frac{\sec\theta(\sec\theta+\tan\theta)}{\sec\theta+\tan\theta}\,d\theta.$$

注意 $(\sec\theta+\tan\theta)'=\sec\theta\tan\theta+\sec^2\theta=\sec\theta(\sec\theta+\tan\theta)$，因此

$$\boxed{\int\sec\theta\,d\theta=\ln|\sec\theta+\tan\theta|+C}.$$

---

英文解析

Common technique: Multiply by $\frac{\sec\theta+\tan\theta}{\sec\theta+\tan\theta}$:

$$\int\sec\theta\,d\theta =\int\frac{\sec\theta(\sec\theta+\tan\theta)}{\sec\theta+\tan\theta}\,d\theta.$$

Note that $(\sec\theta+\tan\theta)'=\sec\theta\tan\theta+\sec^2\theta=\sec\theta(\sec\theta+\tan\theta)$, therefore

$$\boxed{\int\sec\theta\,d\theta=\ln|\sec\theta+\tan\theta|+C}.$$