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  2. List of integrals of trigonometric functions - Wikipedia

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

    Generally, if the function ⁡ is any trigonometric function, and ⁡ is its derivative, ∫ a cos ⁡ n x d x = a n sin ⁡ n x + C {\displaystyle \int a\cos nx\,dx={\frac {a}{n}}\sin nx+C} In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration .

  3. Integration using Euler's formula - Wikipedia

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

    In integral calculus, Euler's formula for complex numbers may be used to evaluate integrals involving trigonometric functions. Using Euler's formula, any trigonometric function may be written in terms of complex exponential functions, namely e i x {\displaystyle e^{ix}} and e − i x {\displaystyle e^{-ix}} and then integrated.

  4. Trigonometric integral - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_integral

    Integral sine in the complex plane, plotted with a variant of domain coloring. Integral cosine in the complex plane. Note the branch cut along the negative real axis. In mathematics, trigonometric integrals are a family of nonelementary integrals involving trigonometric functions.

  5. Tangent half-angle substitution - Wikipedia

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

    The tangent half-angle substitution relates an angle to the slope of a line. Introducing a new variable = ⁡, sines and cosines can be expressed as rational functions of , and can be expressed as the product of and a rational function of , as follows: ⁡ = +, ⁡ = +, = +.

  6. Bioche's rules - Wikipedia

    en.wikipedia.org/wiki/Bioche's_rules

    That is, ω acts like an even function. This is the same as the symmetry of the cosine, which is an even function, so the mnemonic tells us to use the substitution = ⁡ (rule 1). Under this substitution, the integral becomes . The integrand involving transcendental functions has been reduced to one involving a rational function (a constant).

  7. Cozy High-Protein Dump Dinners (Weekly Plan & Shopping List!)

    www.aol.com/cozy-high-protein-dump-dinners...

    For this quick dinner, you’ll start by wilting spinach and then adding lycopene-rich canned crushed tomatoes and fiber-rich chickpeas along with cream to make a sauce. Then comes the fun part ...

  8. Bald eagles soar through snowstorm in Colorado

    www.aol.com/bald-eagles-soar-snowstorm-colorado...

    LAKEWOOD, Colo. – Photos and videos shot in northern Colorado Thursday capture striking images of bald eagles flying through gently falling snow. A snowstorm swept through Colorado this week ...

  9. Integration by reduction formulae - Wikipedia

    en.wikipedia.org/wiki/Integration_by_reduction...

    To compute the integral, we set n to its value and use the reduction formula to express it in terms of the (n – 1) or (n – 2) integral. The lower index integral can be used to calculate the higher index ones; the process is continued repeatedly until we reach a point where the function to be integrated can be computed, usually when its index is 0 or 1.