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\begin{center}
{\Large Warm-Up Problems

January 29, 2003}
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\begin{enumerate}

\item  Verify the following integrals (anti-derivatives) by differentiating.
	Notice the use of the chain rule in your derivatives.
	\begin{enumerate}
	\item  \[ \int 100(20x^4-1)(4x^5-x)^{99} \; dx = (4x^5-x)^{100} + C \]
	\item  \[ \int -\cos(\cos x) \sin x \; dx = \sin(\cos x)+ C \]
	\item  \[ \int \frac{\cos t}{2\sqrt{\sin t +1}} \; dt = \sqrt{\sin t +1} + C \]
	\item  \[ \int \frac{3w^2}{w^3+1}\; dw = \ln(w^3+1)+ C \]
	\item  \[ \int \frac{3}{x} \; dx = \ln(x^3) + C \]
	\item  \[ \int \frac{2x}{\sqrt{1-(x^2+1)^2}} \; dx = \sin^{-1}(x^2+1) + C \]
	\item  \[ \int \frac{4(\tan^{-1} x)^3}{1+x^2} \; dx = (\tan^{-1} x)^4 + C \]
	\end{enumerate}





\end{enumerate}



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