Mastering Integration: Sec u + c Simplified – Rules and Steps

secu+c

To integrate the expression “sec u + c”, we need to use the following rules of integration:

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To integrate the expression “sec u + c”, we need to use the following rules of integration:

1. The integral of sec u is equal to the natural logarithm of the absolute value of the secant of u plus the tangent of u: ∫sec u du = ln|sec u + tan u| + c, where c represents the constant of integration.

2. The integral of a constant term (c) is simply equal to the constant multiplied by the variable, in this case, u: ∫c du = cu + c.

Thus, the integral of “sec u + c” can be broken down into two separate integrals:

∫(sec u) du + ∫c du

Applying the first rule, we have:

= ln|sec u + tan u| + ∫c du

And applying the second rule, we have:

= ln|sec u + tan u| + cu + c

So, the detailed answer for the integral of “sec u + c” is ln|sec u + tan u| + cu + c (where c is the constant of integration).

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