Primitive of Secant Function

Theorem

Secant plus Tangent Form

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

where $\sec x + \tan x \ne 0$.

Tangent plus Angle Form

$\ds \int \sec x \rd x = \ln \size {\map \tan {\frac x 2 + \frac \pi 4} } + C$

Also presented as

Some sources present as the primitive of the reciprocal of the cosine function:

Also see

• Primitive of Sine Function
• Primitive of Cosine Function
• Primitive of Tangent Function
• Primitive of Cotangent Function
• Primitive of Cosecant Function

• Primitive of $\dfrac 1 {\cos a x}$

• Primitive of $\dfrac 1 {\sin a x}$

Sources

• 1945: A. Geary, H.V. Lowry and H.A. Hayden: Advanced Mathematics for Technical Students, Part I ... (previous) ... (next): Chapter $\text {III}$: Integration: Integration
• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Integration
• 1960: Margaret M. Gow: A Course in Pure Mathematics ... (previous) ... (next): Chapter $10$: Integration: $10.4$. Standard integrals: Other Standard Results: $\text {(xx)}$
• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: General Rules of Integration: $14.15$
• 1974: Murray R. Spiegel: Theory and Problems of Advanced Calculus (SI ed.) ... (previous) ... (next): Chapter $5$. Integrals: Integrals of Special Functions: $7$
• 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: $16.15.$