Common integrals table

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[math]\newcommand{\plusc}[1][]{ {\ +C#1} } [/math]



  • [math]\int\text{sin}(x)\mathrm{d}x\eq \cos(x)\plusc{} [/math]
  • [math]\int\cos(x)\mathrm{d}x\eq \sin(x)\plusc{} [/math]

Basic Trigonometric

  • [math]\int\cos^2(x)\mathrm{d}x\eq \frac{\sin(2x)+2x}{4}\plusc{}\eq\frac{\sin(x)\cos(x)+x}{2}\plusc{} [/math]
  • [math]\int\sin^2(x)\mathrm{d}x[/math] [math]\eq \frac{2x-\sin(2x)}{4}\plusc{}\eq x-\frac{x-\sin(x)\cos(x)}{2}\plusc{} [/math]
  • [math]\int\tan^2(x)\mathrm{d}x[/math] ???

Involving: [math]\big(\sqrt{1\pm x^2}\ \big)^{\pm 1} [/math]

  • [math]\int\Big(\sqrt{1-x^2}\Big)\mathrm{d}x[/math] [math]\eq\frac{x\sqrt{1-x^2} + \arcsin(x)}{2} \plusc [/math]