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Standard mathematical integrals

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\(x^n\:dx\)	\(= \frac{x^{n\,+\,1}}{n+1}\) for all values of n except n = - 1
\( \frac{1}{x}\:dx \)	\( = \ln\:x\)
\( e^x\:dx \)	\( = e^x\)
\(\int_{}^{}\sin\:x\:dx \)	\( = -\cos\:x \)
\( \int_{}^{}\cos\:x\:dx \)	\( = \;\sin\:x \)
\( \int \tan\:x\:dx\)	\( = -\ln \cos x \)
\( \int \sec^2\:x\:dx \)	\( = tan\:x \)
\( \int \frac{1}{a^2 + x^2}\:dx \)	\( = \frac{1}{a} \tan^{-1}\frac{x}{a} \)
\( \int \frac{1}{a^2 - x^2}\:dx \)	\(= \frac{1}{2a} \ln \frac{a + x}{a - x} \frac{1}{a} \tanh^{-1}\frac{x}{a} \)
\( \int \frac{1}{x^2 - a^2}\:dx \)	\(= \frac{1}{2\,a} \ln \left(\frac{x-a}{x+a} \right) = -\frac{1}{a} \coth^{-1}\frac{x}{a} \)
\( \int \frac{1}{\sqrt[]{(a^2}-x^2)}\:dx \)	\( = \sin^{-1} \frac{x}{a} \)
\( \int \frac{1}{\sqrt[]{(a^2\:+\:x^2})}\:dx \)	\( = \ln\left(x + \sqrt{(x^2\:+\:a^2)} \right) = \sinh^{-1} \frac{x}{a} \)
\( \int \frac{1}{\sqrt]{(x^2\:-\:a^2)}}\:dx \)	\( = Ln\left(x\:+\:\sqrt{(x^2\:-\:a^2}) \right) \)