Indefinite integrals

Evaluate \[ \int (x^2 + 1)^2 dx \]

There is no integration rule that can be applied to the integrand as it is so expand the integrand.

\[ = \int (x^4 + 2x^2 + 1) dx \]

Use the rules for integrating powers and sums,

\[ \begin{align} &= (\frac{x^5}{5} + 2\frac{x^3}{3} + x) + c \\ \end{align} \ \]

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 \[ \int (2x^2 + x)^2 dx \]