Basic Anti-Derivatives

Question	Answer
\[ \int k \, \textrm{d}x =\]	\[kx +C\]
\[ \int \, \textrm{d}x =\]	\[x +C\]
\[ \int 0 \, \textrm{d}x =\]	\[C\]
\[ \int k \, f(x) \, \textrm{d} x =\]	\[ k \int f(x) \, \textrm{d} x\]
\[ \int \big ( f(x) \pm g(x) \big ) \, \textrm{d} x =\]	\[ \int f(x) \, \textrm{d} x \pm \int g(x) \, \textrm{d} x \]
\[ \int x^n \, \textrm{d} x = \]	\[ \frac {1}{n+1} \, x^{n+1} + C \]
\[ \int \sin(x) \, \textrm{d}x =\]	\[-\cos(x) + C \]
\[ \int \cos(x) \, \textrm{d}x =\]	\[\sin(x) + C \]
\[ \int \sec^2(x) \, \textrm{d}x =\]	\[\tan(x) + C \]
\[ \int \csc^2(x) \, \textrm{d}x =\]	\[-\cot(x) + C \]
\[ \int \sec(x)\tan(x) \, \textrm{d}x =\]	\[\sec(x) + C \]
\[ \int \csc(x)\cot(x) \, \textrm{d}x =\]	\[-\csc(x) + C \]
\[ \sum_{i=1}^n c = \]	\[ n \cdot c \]
\[ \sum_{i=1}^n i = \]	\[ \frac{n(n+1)}{2} \]
\[ \sum_{i=1}^n i^2 = \]	\[ \frac{n(n+1)(2n+1)}{6} \]
\[\int \frac{1}{1+x^2}\,dx=\tan^{-1}x+C\]	\[\tan^{-1}x+C\]

Resource summary

	Created by Bill Andersen about 8 years ago