5.4 Indefinite Integrals and the Net Change Theorem/37

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} \int_{0}^{\frac{\pi}{4}}\left(\frac{1+\cos^2(\theta)}{\cos^2(\theta)}\right)d\theta &= \int_{0}^{\frac{\pi}{4}}\left(\frac{1}{\cos^2(\theta)} + \frac{\cos^2(\theta)}{\cos^2(\theta)}\right)d\theta = \int_{0}^{\frac{\pi}{4}}\left(\sec^2(\theta) + 1\right)d\theta \\[2ex] &= (\tan({\theta}) + \theta)\Bigg|_{0}^{\frac{\pi}{4}}\\[2ex] &= \left[\tan\left({\frac{\pi}{4}}\right) + \frac{\pi}{4}\right] - \left[\tan{0} + 0\right] \\[2ex] &= 1+\frac{\pi}{4} \end{align} }