5.4 Indefinite Integrals and the Net Change Theorem/17

17)$\int {}{}1+tan^{2}x*dx={\frac {d}{dx}}(tan(x))$

${\frac {d}{dx}}(tan(x))={\frac {d}{dx}}\left({\frac {sin(x)}{cos(x)}}\right)={\frac {cos^{2}x-(-(sin(x))(sin(x))}{cos^{2}(x)}}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle ={\frac {cos^{2}x+sin^{2}(x))}{cos^{2}(x)}}={\frac {cos^{2}x}{cos^{2}(x)}}+{\frac {sin^{2}x}{cos^{2}(x)}}}

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

1 3 5 7 8 9 10 11 13 15 17 19 20 21 23 25 27 28 29 31 33 35 37 39 41 53