The integral ∫ sec²x dx equals (for some arbitrary constant K) −(1/(sec x + tan x) + (1/11) − (1/7) (sec x + tan x)² + K).

• The integral ∫ sec²x dx equals (for some arbitrary constant K).
• The result is −(1/(sec x + tan x) + (1/11) − (1/7) (sec x + tan x)² + K).

The integral of sec²x with respect to x can be computed using basic integration techniques. The integral is known to equal:

Integral of sec²x

Mathematically, we express this as:

Result of the Integral

∫ sec²x dx = tan x + C, where C is the constant of integration.

Understanding the Given Expression

You mentioned a more complex expression:

• −(1/(sec x + tan x) + (1/11) − (1/7) (sec x + tan x)² + K)

This expression appears to be a manipulation or transformation of the standard result. It is essential to verify if this transformation holds true through differentiation or by applying integration techniques.

Key Takeaway

Always remember that while integrals can yield various forms, the fundamental result for ∫ sec²x dx remains tan x + C. The additional terms in your expression may arise from specific substitutions or adjustments.