5.4 Indefinite Integrals and the Net Change Theorem/17: Difference between revisions

Revision as of 06:54, 29 August 2022

17) $\int _{}^{}1+tan^{2}xdx$ =

 $\int _{}^{}1+{\frac {sin^{2}x}{cos^{2}x}}dx$  =

$\int _{}^{}{\frac {cos^{2}x+sin^{2}x}{cos^{2}x}}dx$ = $\cos ^{2}x+sin^{2}x=1$ thus, $\int _{}^{}frac{1}{cos^{2}x}dx$

@@ Line 2: / Line 2: @@
   <math>\int_{}^{}1+\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>