## Antiderivatives

 Integral Ans $$x^n$$ $${{x^{n+1}} \over {n+1}}$$ $$\frac{1}{x}$$ $$\ln{|x|}$$ $$e^x$$ $$e^x$$ $$a^x$$ $${a^x \over \ln a}$$  $$x$$ $$\sin x$$ $$\text{-} \cos x$$ $$\cos x$$ $$\sin x$$ $$\tan x$$ $$\text{-} \ln | \cos x ~|$$ $$\sec^2 x$$ $$\tan x$$ $$\csc^2 x$$ $$\text{-} \cot x$$ $$\csc x$$ $$\text{-} \ln | \csc x + \cot x ~| = \ln | \tan \frac{x}{2} |$$ $$\sec x$$ $$\ln | \sec x + \tan x ~|$$ $$\cot x$$ $$\ln | \sin x ~|$$ $$\sec x \tan x$$ $$\sec x$$ $$\csc x \cot x$$ $$\text{-} \csc x$$ $${1 \over \sqrt {1 - x^2} }$$ $$\sin^{-1} x$$ $${\text{-} 1 \over \sqrt {1 - x^2} }$$ $$\cos^{-1} x$$ $${1 \over x^2 + 1}$$ $$\tan^{-1} x$$

$$\int e^{-x} ~dx = -e^{-x} + c$$

$$\ln | \sin x ~| = \text{-} \ln | \csc x ~|$$

$$\ln | \cos x ~| = \text{-} \ln | \sec x ~|$$

$$\ln | \tan x ~| = \text{-} \ln | \tan x ~|$$