Integral Of Secx

The subject of integral of secx encompasses a wide range of important elements. How do I integrate $\\sec(x)$? - Mathematics Stack Exchange. My HW asks me to integrate $\\sin(x)$, $\\cos(x)$, $\\tan(x)$, but when I get to $\\sec(x)$, I'm stuck. integration - When taking the integral of $\sec (x)$, how do you come .... Another key aspect involves, when taking the integral of $\sec (x)$, how do you come up with the crucial step?

Ask Question Asked 9 years, 1 month ago Modified 9 years, 1 month ago Proof of formula for the antiderivative of $\sec x$ [duplicate]. This particular indefinite integral is of significant historical interest too---by construction an antiderivative of $\sec x$ is the function that maps a latitude to its corresponding vertical coordinate in the Mercator projection. Integration of $\sqrt {\sec x}$.

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Instead, you can save this post to reference later. Did I solve the integral of $\ln (\sec x + \tan x)$ correctly?. 4 I attempted this integral, and I got a wildly different answer from wolframalpha, so I couldn't get a proper confirmation whether or not the answer I got is correct. To simplify this integral, first I recalled somewhere from the back of my head that: $$\sec x-\tan x=\tan {x\over 2}$$

How to integrate $\sec^3 x - Mathematics Stack Exchange. Possible Duplicate: Indefinite integral of secant cubed How to integrate $\sec^3 x \, dx$? Can someone please give a method, I tried separating $\sec^3 x$ as $\sec x (\sec^2 x)$ then applying by... Indefinite integral of secant cubed $\\int \\sec^3 x\\>dx$.

The first integral can be solved by $u$-substitution and integration by parts, while the second, is an identity. $$\int\tan (x) \, d\sec (x) = \tan (x)\sec (x)-\int\sec (x) \, d\tan (x)$$ Evaluate: Integral of sec (x) with Complex Analysis. I had seen examples of this with trigonometric identities and I wanted to see how it might do with the integral of $\mathbf {\sec (x)}$, given how its solution involves more than trigonometric functions. In relation to this, integration - How to solve $\int \tan^2 (x) \sec (x) \ dx ....

It's important to note that, how should one solve the following integral? $$\int \tan^2 (x) \sec (x) \ dx$$ I can't think of any substitutions to be made involving $\tan^2 (x)=\sec^2 (x)-1$ or $\sec^2 (x)=\tan^2 (x)+1$, which is how I've been solving most of the similar problems in my book until now. Integrating $\int \tan^2 {x}\sec {x}\ dx$ - Mathematics Stack Exchange. You can always decide whether an indefinite integral is correct by differentiating the answer to see whether you get back the original function.

So, differentiate your answer: do you get $\tan^2x\sec x$?