5.4 Indefinite Integrals and the Net Change Theorem/37

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\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 &=\tan({\theta })+\theta \ {\bigg |}_{0}^{\frac {\pi }{4}}\\[2ex]&=\tan({\frac {\pi }{4}})+{\frac {\pi }{4}}\\[2ex]&=1+{\frac {\pi }{4}}\end{aligned}}}

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 = \int_{0}^{\frac{\pi}{4}}\left(\sec^2(\theta) + 1\right)d\theta }