Single Variable Calculus

Start Free Trial

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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Determine the general indefinite integral $\displaystyle c$

$ \begin{equation} \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} \end{equation} $

Posted on

Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial