فرمول های انتگرال (Integral) شامل ضرب توابع مثلثاتی (Trigonometric Function) و تک جمله ای ها (Monomial)، در ریاضیات (Mathematics)
\[ \int x \cos x \ dx = \cos x + x \sin x \] \[ \int x \cos ax \ dx = \frac{1}{a^2} \cos ax + \frac{x}{a} \sin ax \] \[ \int x^2 \cos x \ dx = 2 x \cos x + \left ( x^2 - 2 \right ) \sin x \] \[ \int x^2 \cos ax \ dx = \frac{2 x \cos ax }{a^2} + \frac{ a^2 x^2 - 2 }{a^3} \sin ax \] \[ \int x^n \cos x dx = -\frac{1}{2}(i)^{n+1}\left [ \Gamma(n+1, -ix) % \right . \nonumber \\ & \left . + (-1)^n \Gamma(n+1, ix)\right] \] \[ \int x^n \cos ax \ dx = \frac{1}{2}(ia)^{1-n}\left [ (-1)^n \Gamma(n+1, -iax) % \right. \nonumber \\ & \left. -\Gamma(n+1, ixa)\right] \] \[ \int x \sin x\ dx = -x \cos x + \sin x \] \[ \int x \sin ax\ dx = -\frac{x \cos ax}{a} + \frac{\sin ax}{a^2} \] \[ \int x^2 \sin x\ dx = \left(2-x^2\right) \cos x + 2 x \sin x \] \[ \int x^2 \sin ax\ dx =\frac{2-a^2x^2}{a^3}\cos ax +\frac{ 2 x \sin ax}{a^2} \] \[ \int x^n \sin x \ dx = -\frac{1}{2}(i)^n\left[ \Gamma(n+1, -ix) %\right. \nonumber \\ & \left. - (-1)^n\Gamma(n+1, -ix)\right] \] \[ \int x \cos^2 x \ dx = \frac{x^2}{4}+\frac{1}{8}\cos 2x + \frac{1}{4} x \sin 2x \] \[ \int x \sin^2 x \ dx = \frac{x^2}{4}-\frac{1}{8}\cos 2x - \frac{1}{4} x \sin 2x \] \[ \int x \tan^2 x \ dx = -\frac{x^2}{2} + \ln \cos x + x \tan x \] \[ \int x \sec^2 x \ dx = \ln \cos x + x \tan x \]
نویسنده علیرضا گلمکانی
شماره کلید 10091
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