Primitive of Tangent Function

Theorem

Secant Form

$\ds \int \tan x \rd x = \ln \size {\sec x} + C$

where $\sec x$ is defined.

Cosine Form

$\ds \int \tan x \rd x = -\ln \size {\cos x} + C$

where $\cos x \ne 0$.

Also see

• Primitive of Sine Function
• Primitive of Cosine Function

• Primitive of Cotangent Function

• Primitive of Secant Function
• Primitive of Cosecant Function

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: General Rules of Integration: $14.13$
• 1974: Murray R. Spiegel: Theory and Problems of Advanced Calculus (SI ed.) ... (previous) ... (next): Chapter $5$. Integrals: Integrals of Special Functions: $5$
• 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 16$: Indefinite Integrals: General Rules of Integration: $16.13.$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $7$: Integrals
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Appendix $8$: Integrals