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

Revision as of 06:07, 29 August 2022

17)<math>\int{}^{}1+tan^2x*dx

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-)<math>\int{}{}1+tan^{2}x*dx = \frac{d}{dx}(tan(x))</math>
+)<math>\int{}^{}1+tan^2x*dx
-<math>\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)}</math>
-<math>=\frac{cos^{2}x+sin^2(x))}{cos^{2}(x)}=\frac{cos^{2}x}{cos^{2}(x)}+\frac{sin^{2}x}{cos^{2}(x)}</math>
-<math>=1+tan^2(x)</math>