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=== [[Goniometrische functie]]s ===
:<math>\int \sin{x}\, {\rm d}x = -\cos{x} + C</math>
:<math>\int \cos{x}\, {\rm d}x = \sin{x} + C</math>
:<math>\int \tan{x} \, {\rm d}x = -\ln{\left| \cos {x} \right|} + C</math>
:<math>\int \cot{x} \, {\rm d}x = \ln{\left| \sin{x} \right|} + C</math>
:<math>\int \sec{x} \, {\rm d}x = \ln{\left| \sec{x} + \tan{x}\right|} + C</math>
:<math>\int \csc{x} \, {\rm d}x = \ln{\left| \csc{x} - \cot{x}\right|} + C</math>
:<math>\int \frac{1}{\sin x}\,{\rm d}x = \ln\left|\tan\tfrac12 x\right|+C = \ln\left|\frac{1}{\sin x}-\cot x\right|+C</math>
:<math>\int \frac{1}{\cos x}\,{\rm d}x = \ln\left|\tan\tfrac12 x+\tfrac14\pi\right|+C = \ln\left|\frac{1}{\cos x}+\tan x\right|+C</math>
:<math>\int \arcsin{\frac{x}{a}}\, {\rm d}x = x\arcsin{\frac{x}{a}}+\sqrt{a^2-x^2} + C,(a>0)</math>
:<math>\int \arccos{\frac{x}{a}}\, {\rm d}x = x\arccos{\frac{x}{a}}-\sqrt{a^2-x^2} + C,(a>0)</math>
:<math>\int \arctan{\frac{x}{a}}\, {\rm d}x = x\arctan{\frac{x}{a}}-\frac{a}{2}\ln\left(a^2+x^2\right)+C ,(a>0)</math>
:<math>\int \frac{1}{\cos^2 x} \, {\rm d}x = \int \sec^2 x \, {\rm d}x = \tan x + C</math>
:<math>\int \frac{1}{\sin^2 x} \, {\rm d}x = \int \csc^2 x \, {\rm d}x = -\cot x + C</math>
:<math>\int \sec{x} \, \tan{x} \, {\rm d}x = \sec{x} + C</math>
:<math>\int \csc{x} \, \cot{x} \, {\rm d}x = - \csc{x} + C</math>
:<math>\int \sin^2 x \, {\rm d}x = \tfrac12(x - \sin x \cos x) + C</math>
:<math>\int \cos^2 x \, {\rm d}x = \tfrac12(x + \sin x \cos x) + C</math>
:<math>\int \sin^n x \, {\rm d}x = - \frac{\sin^{n-1} {x} \cos {x}}{n} + \frac{n-1}{n} \int \sin^{n-2}{x} \, {\rm d}x</math>
:<math>\int \cos^n x \, {\rm d}x = \frac{\cos^{n-1} {x} \sin {x}}{n} + \frac{n-1}{n} \int \cos^{n-2}{x} \, {\rm d}x</math>
:<math>\int \tan^n x \, {\rm d}x = \frac{\tan^{n-1}x}{n-1}-\int\tan^{n-2}x \, {\rm d}x ,(n\neq1)</math>
:<math>\int \cot^n x \, {\rm d}x = -\frac{\cot^{n-1}x}{n-1}-\int \cot^{n-2}x \, {\rm d}x ,(n\neq1)</math>
:<math>\int \sec^n x \, {\rm d}x = \frac{\tan x\sec^{n-2}x}{n-1}+\frac{n-2}{n-1}\int \sec^{n-2}x \, {\rm d}x,(n\neq1)</math>
:<math>\int \csc^n x \, {\rm d}x = -\frac{\cot x\csc^{n-2}x}{n-1}+\frac{n-2}{n-1}\int \csc^{n-2}x \, {\rm d}x,(n\neq1)</math>
:<math>\int \sin ax\sin bx\,{\rm d}x = \frac{\sin(a-b)x}{2(a-b)}-\frac{\sin(a+b)x}{2(a+b)}+C,(a^2\neq b^2)</math>
:<math>\int \sin ax\cos bx\,{\rm d}x = -\frac{\cos(a-b)x}{2(a-b)}-\frac{\cos(a+b)x}{2(a+b)}+C,(a^2\neq b^2)</math>
=== [[Hyperbolische functie]]s ===
:<math>\int \sinh x \, {\rm d}x = \cosh x + C</math>
:<math>\int \cosh x \, {\rm d}x = \sinh x + C</math>
:<math>\int \tanh x \, {\rm d}x = \ln |\cosh x| + C</math>
:<math>\int \mboxoperatorname{csch}\,x \, {\rm d}x = \ln\left| \tanh {x \over2}\right| + C</math>
:<math>\int \mboxoperatorname{sech}\,x \, {\rm d}x = \arctan(\sinh x) + C</math>
:<math>\int \coth x \, {\rm d}x = \ln|\sinh x| + C</math>
:<math>\int \sinh^2 x \, {\rm d}x = \frac{1}{4}\sinh 2x-\frac{1}{2}x + C</math>
:<math>\int \cosh^2 x \, {\rm d}x = \frac{1}{4}\sinh 2x+\frac{1}{2}x + C</math>
:<math>\int \mboxoperatorname{sech}^2 x \, {\rm d}x = \tanh x + C</math>
:<math>\int \sinh^{-1}\frac{x}{a} \, {\rm d}x = x\sinh^{-1}\frac{x}{a}-\sqrt{x^2+a^2} + C</math>
:<math>\int \cosh^{-1}\frac{x}{a} \, {\rm d}x = x\cosh^{-1}\frac{x}{a}-\sqrt{x^2-a^2} + C \left(\cosh^{-1}\frac{x}{a}>0,a>0\right)</math>
:<math>\int \cosh^{-1}\frac{x}{a} \, {\rm d}x = x\cosh^{-1}\frac{x}{a}+\sqrt{x^2-a^2} + C \left(\cosh^{-1}\frac{x}{a}<0,a>0\right)</math>
:<math>\int \tanh^{-1}\frac{x}{a} \, {\rm d}x = x\tanh^{-1}\frac{x}{a}+\frac{a}{2}\ln\left|a^2-x^2\right|+C</math>
:<math>\int \mboxoperatorname{sech}x\tanh x\,{\rm d}x = -\mboxoperatorname{sech}x+C</math>
:<math>\int \mboxoperatorname{csch}x\coth x\,{\rm d}x = -\mboxoperatorname{csch}x+C</math>
{{Navigatie lijsten van integralen}}
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