Primitive of Reciprocal of Tangent of a x

Theorem

$\ds \int \frac {\d x} {\tan a x} = \frac 1 a \ln \size {\sin a x} + C$

Proof

\(\ds \int \frac {\d x} {\tan a x}\)

\(=\)

\(\ds \int \cot a x \rd x\)

Cotangent is Reciprocal of Tangent

\(\ds \)

\(=\)

\(\ds \frac 1 a \ln \size {\sin a x} + C\)

Primitive of $\cot a x$

$\blacksquare$

Also see

• Primitive of $\dfrac 1 {\sin a x}$

• Primitive of $\dfrac 1 {\cos a x}$

• Primitive of $\dfrac 1 {\cot a x}$

• Primitive of $\dfrac 1 {\sec a x}$

• Primitive of $\dfrac 1 {\csc a x}$

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: Integrals involving $\tan a x$: $14.434$