# Single Variable Calculus, Chapter 5, 5.4, Section 5.4, Problem 18

## Expert Answers

Determine the general indefinite integral $\displaystyle c$

\begin{aligned} \int (1-x^2)^2 dx &= \int \left( 1 - 2x^2 + x^4 \right) dx \\ \\ \int (1-x^2)^2 dx &= \int 1 dx - 2 \int x^2 dx + \int x^4 dx\\ \\ \int (1-x^2)^2 dx &= x - 2 \left( \frac{x^{2+1}}{2+1} \right) + \left( \frac{x^{4+1}}{4+1} \right) + C\\ \\ \int (1-x^2)^2 dx &= x - \frac{2x^3}{3} + \frac{x^5}{5} + C \end{aligned}

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