5.4 Indefinite Integrals and the Net Change Theorem/17: Difference between revisions
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<math>\int_{}^{}1+tan^2xdx = | |||
\int_{}^{}1+\frac{sin^2x}{cos^2x}dx = | \int_{}^{}1+\frac{sin^2x}{cos^2x}dx = | ||
Revision as of 17:41, 13 September 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \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\int _{}^{}{\frac {1}{cos^{2}x}}dx=\int _{}^{}\sec ^{2}xdx=tanx+C}