Chapter 7 - Section 7.5 - Strategy for Integration - 7.5 Exercises - Page 508: 37

$$\int_{0}^{\frac{\pi}{4}}\tan ^{3}\theta\sec ^{2}\theta d\theta=\frac{1}{4}$$

$$\int_{0}^{\frac{\pi}{4}}\tan ^{3}\theta\sec ^{2}\theta d\theta=\int_{0}^{\frac{\pi}{4}}\tan ^{3}\theta d\tan \theta$$ $$=\left [ \frac{\tan ^{4} \theta}{4} \right ]_{0}^{\frac{\pi}{4}}$$ $$=\frac{1}{4}$$