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

Revision as of 07:16, 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,

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

$\int _{}^{}\sec ^{2}xdx$ =

$tanx+C$

@@ Line 11: / Line 11: @@
 <math>\int_{}^{}\sec^2xdx</math> =
 <math>tanx+C</math>
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