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This page lists some of the most common antiderivatives; a more complete list can be found in the List Of Integrals . We use ''C'' for an Arbitrary Constant Of Integration that can only be determined if something about the value of the integral at some point is known. Thus each function has an infinite number of antiderivatives. These formulas only state in another form the assertions in the Table Of Derivatives . RULES FOR INTEGRATION OF GENERAL FUNCTIONS :$\backslash int\; af(x)\backslash ,dx\; =\; a\backslash int\; f(x)\backslash ,dx$ :$\backslash int+\; g(x)\backslash ,dx\; =\; \backslash int\; f(x)\backslash ,dx\; +\; \backslash int\; g(x)\backslash ,dx$ :$\backslash int\; f(x)g(x)\backslash ,dx\; =\; f(x)\backslash int\; g(x)\backslash ,dx\; -\; \backslash int\; \backslash left(\backslash int\; g(x)\backslash ,dx\; ight)\backslash ,d(f(x))$ INTEGRALS OF SIMPLE FUNCTIONS Rational Function s more integrals: List Of Integrals Of Rational Functions :$\backslash int\; \backslash ,dx\; =\; x\; +\; C$ : e -1

Irrational Function s


:$\backslash int\; \{dx\; \backslash over\; \backslash sqrt\{a^2-x^2\}\}\; =\; \backslash arcsin\; \{x\; \backslash over\; a\}\; +\; C$
:$\backslash int\; \{-dx\; \backslash over\; \backslash sqrt\{a^2-x^2\}\}\; =\; \backslash arccos\; \{x\; \backslash over\; a\}\; +\; C$


Trigonometric Function s


:$\backslash int\; \backslash sin\{x\}\backslash ,\; dx\; =\; -\backslash cos\{x\}\; +\; C$
:$\backslash int\; \backslash cos\{x\}\backslash ,\; dx\; =\; \backslash sin\{x\}\; +\; C$
:$\backslash int\; \backslash sec^2\; x\; \backslash ,\; dx\; =\; an\; x\; +\; C$
:$\backslash int\; \backslash csc^2\; x\; \backslash ,\; dx\; =\; -\backslash cot\; x\; +\; C$
:$\backslash int\; \backslash sec\{x\}\; \backslash ,\; an\{x\}\; \backslash ,\; dx\; =\; \backslash sec\{x\}\; +\; C$
:$\backslash int\; \backslash csc\{x\}\; \backslash ,\; \backslash cot\{x\}\; \backslash ,\; dx\; =\; -\; \backslash csc\{x\}\; +\; C$
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:$\backslash int\_\{0\}^\{2\; \backslash pi\}\; e^\{x\; \backslash cos\; heta\}\; d\; heta\; =\; 2\; \backslash pi\; I\_\{0\}(x)$ (where $I\_\{0\}(x)$ is the modified Bessel Function of the first kind)

:$\backslash int\_\{0\}^\{2\; \backslash pi\}\; e^\{x\; \backslash cos\; heta\; +\; y\; \backslash sin\; heta\}\; d\; heta\; =\; 2\; \backslash pi\; I\_\{0\}\; \backslash left(\; \backslash sqrt\{x^2\; +\; y^2\}\; ight)$