Integral of Sec x by Partial Method
Integral of secant function ∫(sec x).dx, can be evaluated using the partial fraction decomposition method with the following steps:
Step 1: Rewrite sec(x) as 1/cos(x)
Step 2: Express 1/cos(x) as (A/cos(x) + B/sin(x)
Step 3: Multiply both sides by cos(x) to eliminate the denominator and then separately set (x = 0) and (x = π/2) to solve for (A) and (B).
Step 4: Rewrite (∫sec(x), dx as ∫Acos(x) + Bsin(x) dx.
Step 5: Integrate Acos(x) and Bsin(x) separately. This yields (A ln| sec(x) + tan(x)|) and (-B ln| csc(x) + cot(x)|) respectively.
Step 6: Combine the two integrals to get the final result.
Here, integral of secant function using the partial fraction decomposition method:
∫sec (x)dx = A.ln|sec x + tan x| – B.ln|cosec x + cot x| + C
where,
- A and B are constants Determined from Partial Fraction Decomposition
- C is Constant of Integration
Integral of Sec x
Integral of sec x is ∫(sec x).dx = ln| sec x + tan x| + C. Integration of the secant function, denoted as ∫(sec x).dx and is given by: ∫(sec x).dx = ln| sec(x) + tan(x)| + C. Sec x is one of the fundamental functions of trigonometry and is the reciprocal function of Cos x. Learn how to integrate sec x in this article.
In this article, we will understand the formula of the integral of sec x, Graph of Integral of sec x, and Methods of Integral of sec x.
Table of Content
- What is Integral of Sec x?
- Integral of Sec x Formula
- Integral of Sec x by Substitution Method
- Integral of Sec x by Partial Method
- Integral of Sec x by Trigonometric Formula
- Integral of Sec x by Hyperbolic Functions
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