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Question
\[\int\frac{1 - x^4}{1 - x} \text{ dx }\]
Sum
Solution
\[\int\left( \frac{1 - x^4}{1 - x} \right)dx\]
\[ = \int\frac{\left( 1 - x^2 \right) \left( 1 + x^2 \right)}{\left( 1 - x \right)}dx\]
\[ = \int\frac{\left( 1 - x \right) \left( 1 + x \right) \left( 1 + x^2 \right)}{\left( 1 - x \right)}dx\]
\[ = \int\left( 1 + x \right) \left( 1 + x^2 \right)dx\]
\[ = \int\left( 1 + x^2 + x + x^3 \right)dx\]
\[ = x + \frac{x^3}{3} + \frac{x^2}{2} + \frac{x^4}{4} + C\]
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