5.4 Indefinite Integrals and the Net Change Theorem/17: Difference between revisions
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\int(1+\tan^2{\alpha})\,d\alpha = \int\left(1+\frac{sin^2\alpha}{cos^2\alpha}\right)d\alpha = \int\left(\frac{cos^2\alpha+sin^2\alpha}{cos^2\alpha}\right)d\alpha = \int\frac{1}{cos^2\alpha}d\alpha = | \int(1+\tan^2{\alpha})\,d\alpha = \int\left(1+\frac{sin^2\alpha}{cos^2\alpha}\right)d\alpha = \int\left(\frac{cos^2\alpha+sin^2\alpha}{cos^2\alpha}\right)d\alpha = \int\frac{1}{cos^2\alpha}d\alpha = | ||
\int\sec^2\alpha \,d\alpha = | \int\sec^2\alpha \,d\alpha = \tan{alpha}+C | ||
\tan{ | |||
</math> | </math> | ||
Note: <math>\cos^2\alpha+sin^2\alpha=1</math> | Note: <math>\cos^2\alpha+sin^2\alpha=1</math> | ||
Revision as of 17:50, 13 September 2022
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int(1+\tan^2{\alpha})\,d\alpha = \int\sec^2\alpha \,d\alpha = \tan\alpha + C }
Note:
Or,
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int(1+\tan^2{\alpha})\,d\alpha = \int\left(1+\frac{sin^2\alpha}{cos^2\alpha}\right)d\alpha = \int\left(\frac{cos^2\alpha+sin^2\alpha}{cos^2\alpha}\right)d\alpha = \int\frac{1}{cos^2\alpha}d\alpha = \int\sec^2\alpha \,d\alpha = \tan{alpha}+C }
Note: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \cos^2\alpha+sin^2\alpha=1}