How would you solve the integral000which are all easy integrals, so the answer is− − In x + x + CPick ONE of these answers.This is just the derivative of a natural logarithm, so the answer is In x² - 4x + 8 + CBy completing the square in the denominator and substituting with a tan 0; (in this case x - 2 = 2 tan 0)Add and subtract x² on the top of the fraction and then split into two integrals;This is equal todxS² - S ² + S ²4,4x· 27² √ ² - 57²² S = 857²S-77²² S+164x+8By factoring the denominator x² - 4x + 8 = (x − a) (x − b) and then using partial fractions;This is equal tox²+4Jx+2'x²which are all easy integrals, so the answer istan ¹()- Inr+2+C-1dx4x + 8

The denominator of the integrand is .Write is as,

Answered: How would you solve the integral S x²…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Related questions

Question

How would you solve the integral
000
which are all easy integrals, so the answer is
− − In x + x + C
Pick ONE of these answers.
This is just the derivative of a natural logarithm, so the answer is In x² - 4x + 8 + C
By completing the square in the denominator and substituting with a tan 0; (in this case x - 2 = 2 tan 0)
Add and subtract x² on the top of the fraction and then split into two integrals;
This is equal to
dx
S² - S ² + S ²4,
4x
· 27² √ ² - 57²² S = 857²S-77²² S
+16
4x+8
By factoring the denominator x² - 4x + 8 = (x − a) (x − b) and then using partial fractions;
This is equal to
x²+4
J
x+2'
x²
which are all easy integrals, so the answer is
tan ¹()- Inr+2+C
-1
dx
4x + 8

Expert Solution

Step 1: Observe denominator of the integrand of integral

The denominator of the integrand is $x squared minus 4 x plus 8$ .

Write is as,

$x squared minus 4 x plus 8 equals x squared minus 4 x plus 4 plus 4 x squared minus 4 x plus 8 equals bold italic x to the power of bold 2 bold minus bold 2 bold left parenthesis bold 2 bold right parenthesis bold left parenthesis bold italic x bold right parenthesis bold plus bold 2 to the power of bold 2 plus 4 x squared minus 4 x plus 8 equals bold left parenthesis bold italic x bold minus bold 2 bold right parenthesis to the power of bold 2 plus 4$