## sec x + c

### In mathematics, “sec x” is the reciprocal of the cosine function, defined as 1/cos x

In mathematics, “sec x” is the reciprocal of the cosine function, defined as 1/cos x. The term “c” can be interpreted as a constant, typically used in indefinite integrals.

If you are asked to find the integral (antiderivative) of “sec x + c” with respect to x, where c is a constant, then the solution involves finding the antiderivative of sec x, which is typically expressed as “ln|sec x + tan x|”.

To demonstrate this, we can start by finding the antiderivative of sec x:

∫ sec x dx = ln|sec x + tan x| + C

The “+ C” term indicates the constant of integration, which accounts for the fact that the antiderivative is not unique.

Now, if we have the expression “sec x + c”, where c is a constant, the antiderivative can be obtained in a similar manner:

∫ (sec x + c) dx = ∫ sec x dx + ∫ c dx

Using the linearity property of integration, we can split the integral:

= ln|sec x + tan x| + cx + K

where K is the constant of integration, which combines the constants C and the contribution from ∫ c dx.

In summary, the integral of “sec x + c”, where c is a constant, is equal to ln|sec x + tan x| + cx + K, where K represents the constant of integration.

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Simplified Expression: -tan(x)/(1 + cot^2(x)) + c