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How do I prove that indefinite integral of $\sec x$ is equal to $\ln(\sec x + \tan x) + C$? I tried to substitute $t = \cos x$ but that didn't help. I have no idea how to integrate it any other way, and my textbook doesn't offer a derivation.
Since the derivative of is , the integral of is . The answer is the antiderivative of the function. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.
The formula for the antiderivative product rule is ∫f(x).g(x) dx = f(x) ∫g(x) dx − ∫(f′(x) [ ∫g(x) dx)]dx + C where we need to find the antiderivative of the product of two or more functions.
26 Ιουλ 2024 · Answer: The integral of sec x is ln|sec(x) + tan(x)| + C, where C is the constant of integration.∫ sec(x) dx = ln ∣sec(x) + tan(x)∣ + C The integral of sec(x) with respect to x can be found by recognizing its antiderivative.
What is the Integral of Sec x? The integral of sec x is ln|sec x + tan x| + C. It denoted by ∫ sec x dx. This is also known as the antiderivative of sec x. We have multiple formulas for this. But the more popular formula is, ∫ sec x dx = ln |sec x + tan x| + C. Here "ln" stands for natural logarithm and 'C' is the integration constant.
Here is a list of the antiderivatives presented in this lecture: 1. sin xdx = − cos x + c where c is any constant. xn+1 2. x n dx = n + 1 + c for n = −1. dx 3. x = ln |x| + c (This takes care of the exceptional case n = −1 in 2.) 4. sec 2 xdx = tan x + c. 5. dx √ = sin−1 x + c (where sin−1 x denotes “inverse sine” or arcsin, 1 ...
