Sep 27, 2013 · My HW asks me to integrate $\sin (x)$, $\cos (x)$, $\tan (x)$, but when I get to $\sec (x)$, I'm stuck.

Immediate calculation of $$\int \sec ^ {3}xdx.$$ We need the basic formulas of the first two derivatives of $\sec x:$\begin {eqnarray*} (\sec x)^ {\prime } &=&\sec x ...

Oct 6, 2016 · It t ook a long time for that particular integral to be solved. So I'd say you really just have to guess it. But once you've seen it, you understand why it is good guess given you know the …

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...

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 …

Sep 21, 2013 · Is it possible to solve $\int \sec^2 x ~dx$ without knowing that $\frac {d} {dx}\tan x = \sec^2 x$?

$\int\sec^3x\,dx$; the integral of a function raised to some power is equal to a fraction of the sum of its integral and its derivative.

Nov 27, 2023 · The best approach is to treat the $\sec x < 0$ case as a separate integration from the $\sec x>0$ case. So you do consider $\sqrt {\sec^ {2}x}=\sec (x)$. Then you consider $\sqrt {\sec^ …

May 8, 2018 · While practicing for the AP exam, I came across an integral that I found interesting and I attempted to do by hand: $$\\int(\\sec^4 x)\\, dx$$ Eventually I got stuck, but here are the steps I took …

Jun 29, 2017 · Admittedly the expression thus obtained for the antiderivative is $\ln\left|\frac {1+\tan\frac {x} {2}} {1-\tan\frac {x} {2}}\right|+C$ instead of $\frac12\ln\left|\frac {1+\sin x} {1-\sin x}\right|+C$ or …