Indefinite integrals

 

Evaluate \[ \int (7x^3 + \frac{1}{2}x^2) dx \]

Use the basic integration rules to change the form of the integrand.

\[ \int (7x^3 + \frac{1}{2}x^2) dx = 7 \int x^3 dx + \frac{1}{2} \int x^2 dx \]

Use the rule for integrating a power,

\[ = 7 \frac{x^{3+1}}{3+1} + \frac{x^{2+1}}{2(2+1)} + c \]

Now simplify the expression

\[ = \frac{7x^4}{4} + \frac{x^3}{6} + c \]

You will gain most benefit if you work through each problem first and then come back and check your work against the solution.

 

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Now You Try:

Evaluate \[ \int (5x^4 + 3x^2) dx \]