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Worksheet on Integration Rules

MAT 1161

Sean Forman

April 28, 2003

For each of the following below, find the integral, $\int f(x) dx$.

1. $\int (3x^6 + 5x^2 + 4x) dx$

   
   
   
   
   
   
   

2. $\int e^{4x} dx$

   
   
   
   
   
   
   

3. $\int 5\frac{1}{\sqrt[3]{x}} dx$

   
   
   
   
   
   
   

4. $\int \frac{7}{4x} dx$

   
   
   
   
   
   
   

5. $\int \frac{3x^2}{x^3 + 6} dx$

   
   
   
   
   
   
   

6. $\int (x^3 + 4 x^2 - 12x)^5(3x^2 + 8x - 12) dx$

   
   
   
   
   
   
   

7. $\int \sqrt{3x^2 + 6x + 9} (x + 1) dx$

For each problem, find the value of the definite integral.

1. $\int_{0}^{2} x^6 dx$
   

   
   
   
   
   
   
   

2. $\int_{0}^{2} x^{4.2} dx$

   
   
   
   
   
   
   

3. $\int_{1}^{e} \frac{7}{4x} dx$

   
   
   
   
   
   
   

4. $\int_{0}^{2} 6e^{3x} dx$

   
   
   
   
   
   
   

5. $\int_{1}^{2} \frac{3}{x^4} dx$

   
   
   
   
   
   
   

6. $\int_{1}^{4} (\sqrt{x} - \frac{1}{x^2}) dx$