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x^{2}-x-6=0 -x+3\gt 2x+1 ; line\:(1,\:2),\:(3,\:1) f(x)=x^3 ; prove\:\tan^2(x)-\sin^2(x)=\tan^2(x)\sin^2(x) \frac{d}{dx}(\frac{3x+9}{2-x}) (\sin^2(\theta))' \sin(120)
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The integral of the secant function was historically one of the first integrals of its type ever evaluated, before most of the development of integral calculus. It is important because it is the vertical coordinate of the Mercator projection, used for marine navigation with constant compass bearing.
21 Σεπ 2013 · To integrate $\tan^{2}(x)$ you can add and subtract 1 to obtain a tangent as part of your anti derivative. The "subtraction" of 1 cancels against the second fraction after the split. Share
Integral of Secant sec x dx =? This calculation is not as straightforward as the one for the tangent function. What we need to do is add together the formulas for the derivatives of the secant and tangent functions. d 2 (sec x + tan x) = sec x + sec x tan x dx = (sec x)(sec x + tan x)
We begin by writing the indefinite integral for secant as $$\int \sec x \, dx = \int \frac{\sec^2 x}{\sec x} \, dx = \int \frac{d(\tan x)}{\sec x}.$$ Now let $x = \sinh u, d(\tan x) = \cosh u$, and it is not too hard to see that $\sec x = \sinh u$.
