5.4 Indefinite Integrals and the Net Change Theorem/17

17. \begin{align}

<math>\int_{}^{}1+tan^2 x\,dx <math> <math>\int1+\frac{sin^2x}{cos^2x}\,dx<math> <math>\int\frac{cos^2x+sin^2x}{cos^2x}\,dx<math> <math>\cos^2x+sin^2x=1<math>, thus <math>\int\frac{1}{cos^2x}\,dx<math> <math>\int\sec^2x\,dx<math> <math>tanx+C\<math> \end{align}