Primitive of Sine of a x over Cosine of a x
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Theorem
- $\ds \int \dfrac {\sin a x} {\cos a x} \rd x = -\dfrac 1 a \ln \size {\cos a x} + C$
Proof
\(\ds \int \dfrac {\sin a x} {\cos a x} \rd x\) | \(=\) | \(\ds \int \cot a x \rd x\) | Tangent is Sine divided by Cosine | |||||||||||
\(\ds \) | \(=\) | \(\ds -\dfrac 1 a \ln \size {\cos a x} + C\) | Primitive of $\tan a x$: Cosine Form |
$\blacksquare$
Also see
Sources
- 1968: George B. Thomas, Jr.: Calculus and Analytic Geometry (4th ed.) ... (previous) ... (next): Front endpapers: A Brief Table of Integrals: $67$.