Online Math Tutor LLC

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Online Math Tutor LLC

Discover the Path to Mathematical Mastery 
An Education That Counts

Practice Problems: Chain Rule

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Practice Problems

Answer the following questions by using the integration technique known as u-substitution.  

  1. \(\displaystyle \int (2x+1)^2dx\)
  2. \(\displaystyle \int x\sqrt{2x+3}dx\)
  3. \(\displaystyle \int \frac{x}{2x+1}dx\)
  4. \(\displaystyle \int \frac{x^3}{x^2-4}dx \)
  5. \(\displaystyle \int x^2\texttt{e}^{2x^3+1} dx \)
  1. \(\displaystyle \int {\frac{\texttt{e}^{2x}}{1+\texttt{e}^{2x}}} dx \)
  2. \(\displaystyle \int_1^\texttt{e} {\frac{\texttt{ln}(x)}{x} dx} \)
  3. \(\displaystyle \int {\frac{\texttt{sin}(x)}{1+\texttt{cos}(x)}} dx \)
  4. \(\displaystyle \int {\frac{\texttt{e}^x}{1+\texttt{e}^{2x}}} dx \)
  5. \(\displaystyle \int {\frac{dx}{\texttt{e}^x + \texttt{e}^{-x}}} \)
  1. \(\displaystyle \int {\frac{dx}{\sqrt{x}(x+1)}} \)
  2. \(\displaystyle \int {\frac{x}{\sqrt{1-x^4}}} dx \)
  3. \(\displaystyle \int {\frac{x^2}{x^2+1}} dx \)

Suggestive Solution Guide