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  2. Tangent half-angle substitution - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle...

    The tangent of half an angle is important in spherical trigonometry and was sometimes known in the 17th century as the half tangent or semi-tangent. [2] Leonhard Euler used it to evaluate the integral ∫ d x / ( a + b cos ⁡ x ) {\textstyle \int dx/(a+b\cos x)} in his 1768 integral calculus textbook , [ 3 ] and Adrien-Marie Legendre described ...

  3. Integration using Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Integration_using_Euler's...

    At this point we can either integrate directly, or we can first change the integrand to 2 cos 6x − 4 cos 4x + 2 cos 2x and continue from there. Either method gives Either method gives ∫ sin 2 ⁡ x cos ⁡ 4 x d x = − 1 24 sin ⁡ 6 x + 1 8 sin ⁡ 4 x − 1 8 sin ⁡ 2 x + C . {\displaystyle \int \sin ^{2}x\cos 4x\,dx=-{\frac {1}{24 ...

  4. List of integrals of trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    For the special antiderivatives involving trigonometric functions, see Trigonometric integral. [ 1 ] Generally, if the function sin ⁡ x {\displaystyle \sin x} is any trigonometric function, and cos ⁡ x {\displaystyle \cos x} is its derivative,

  5. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful.

  6. Americans get too much omega-6 and not enough omega-3 ... - AOL

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    December 24, 2024 at 12:26 PM. ... Stir 1 to 2 tablespoons of chia or flaxseeds (omega-3s) into oatmeal, smoothies or yogurt. ... Stock market today: Equities attempt rebound ahead of earnings season.

  7. List of integrals of rational functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    Integrands of the form x m (a + b x n + c x 2n) p when b 2 − 4 a c = 0 [ edit ] The resulting integrands are of the same form as the original integrand, so these reduction formulas can be repeatedly applied to drive the exponents m and p toward 0.

  8. 11 Fast-Food Soups, Ranked Best to Worst - AOL

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    2. Chick-fil-A Chicken Noodle Soup. Price: $4.15 cup / $6.35 bowl Chick-fil-A’s chicken noodle soup is leagues better than it has any right to be. There’s so much flavor in this broth, and the ...

  9. Wendy’s is offering 12 days of free food in December - AOL

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    Wendy’s is caroling door-to-door with buy-one, get-one-free deals including Breakfast Baconator, Saucy Nuggs, Dave's Single and more.