   Chapter 7.3, Problem 28E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ x 2 + 1 ( x 2 − 2 x + 2 ) 2   d x

To determine

To Find:x2+1(x22x+2)2dx

Explanation

Calculation: Given x2+1(x22x+2)2dx

Rewrite the integral by completing the square

x2+1(x22x+2)2dx

x2+1((x22x+1)+21)2dx

x2+1((x21)2+1)2dx

Now do following trigonometric substitution

x1=tanθx=tanθ+1dx=sec2θdθto get((tanθ+1)2+1)sec2θ((tanθ)2+1)2dθ

((tanθ+1)2+1)sec2θsec4θdθ

((tanθ+1)2+1)sec2θdθ

tan2θ+2tanθ+2sec2θdθ

Rewrite the integral in terms of θ and simplify

tan2θsec2θdθ+2tanθsec2θdθ+2sec2θdθ

sin2θdθ+2sinθcosθdθ+2cos2θdθ

121cos2θdθ+sin2θdθ+1+cos2θdθ

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find f. f(t) = t2 + 1/t2, t 0, f(2) = 3, f(1) = 2

Single Variable Calculus: Early Transcendentals, Volume I

#### Expand each expression in Exercises 122. (3x+1)(2x2x+1)

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Find the distance between (2, 4) and (6, 8).

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Find the limit. limxln(sinx)

Single Variable Calculus: Early Transcendentals

#### For y=43+2x, y = _____. a) 4(3 + 2x)3/2 b) 4(3 + 2x)3/2 c) 2(3 + 2x)1/2 d) 2(3 + 2x)1/2

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 