5.4 Indefinite Integrals and the Net Change Theorem/17

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int (1+\tan ^{2}{\alpha })\,d\alpha =\int \sec ^{2}\alpha \,d\alpha =\tan \alpha +C}

Note: $1+\tan ^{2}{\alpha }=\sec ^{2}\alpha$

Or,

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_{}^{}1+tan^2xdx = \int_{}^{}1+\frac{sin^2x}{cos^2x}dx = \int_{}^{}\frac{cos^2x+sin^2x}{cos^2x}dx \cos^2x+sin^2x=1 \int_{}^{}\frac{1}{cos^2x}dx = \int_{}^{}\sec^2xdx = tanx+C }