Single Variable Calculus

Start Free Trial

Single Variable Calculus, Chapter 7, 7.6, Section 7.6, Problem 70

Expert Answers

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

Evaluate the integral $\displaystyle \int \frac{x}{1 + x^4} dx$

If we let $u = x^2$, then

$du = 2x dx$

So,

$ \begin{equation} \begin{aligned} \int \frac{x}{1 + x^4} dx = \int \frac{x}{1 + (x^2)^2} dx &= \frac{1}{2} \int \frac{du}{1 + (u)^2}\\ \\ \text{recall that } \frac{d}{dx} \left( \tan^{-1}(x) \right) &= \frac{1}{1+x^2}\\ \\ &= \frac{1}{2} \tan^{-1} u + c\\ \\ &= \frac{1}{2} \tan^{-1} (x^2) + 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

Already a member? Log in here.

Are you a teacher? Sign up now