Calculus 2

Can someone please show and explain step by step how to evaluate this integral?

Problem #1)∫ 1/(x^3+x^2+x+1) dx

This is what I got so far. I am not sure what to do thereafter after doing partial fraction decomposition (in which I got A = 1/2, B = 1/2, and C = 1/2)

1/(x^2+1)(x+1) = ∫(-1/2x)+(1/2)/(x^2+1) + ((1/2)/(x+1)) dx

  1. 👍 0
  2. 👎 0
  3. 👁 191
  1. First step:
    decompose into partial fractions (probably the hardest part of the problem)
    Factorize the denominator (if possible)
    x^3+x^2+x+1=x^2(x+1)+1(x+1)=(x^2+1)(x+1)
    so we can decompose the given fraction into:
    1/(x^3+x^2+x+1)
    =1/2(x+1) + (1-x)/2(x^2+1)
    which can be integrated readily.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    Consider the sequence of steps to solve the equation: 2(x − 4) + 6x = 9x − 10 Which step in solving this equation is justified by the Commutative Property of Addition? Given ⇒ 2(x − 4) + 6x = 9x − 10 Step 1 ⇒ 2x − 8

    asked by Anonymous on October 25, 2018
  2. Math

    evaluate the expression ₆ P ₀ I am not sure how to do this problem can some one show me how to do this step by step

    asked by Iva on December 12, 2011
  3. math

    Consider the sequence of steps to solve the equation: 5(x - 3) = 7x 2 Step 1 ⇒ 10(x - 3) = 7x Step 2 ⇒ 10x - 30 = 7x Step 3 ⇒ 3x - 30 = 0 Step 4 ⇒ 3x = 30 Step 5 ⇒ x = 10 Identify the property of equality which yields

    asked by Valerie on October 22, 2019
  4. Calculus

    Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if it is convergent or divergent). I know how to find the indefinite integral of csc(x) dx, but I do not know how to evaluate the improper integral, at the

    asked by Sam on June 5, 2012
  5. ALGEBRA HELP

    When solving the equation, what property was used to go from step 3 to step 4? Step 1: -(2x+3= x-18 Step 2: -2x-3=x-18 Step 3: -3=3x-18 Step 4: 15=3x A)APOE B)SPOE C)MPOE D)DPOE

    asked by cv on October 21, 2013
  1. math

    An equation and the steps to solve it are shown below: 3x − one over two (8x − 2) = 4 Step 1: 3x − 4x + 1 = 4 Step 2: x + 1 = 4 Step 3: x + 1 − 1 = 4 − 1 Step 4: x = 3 Which step was the error made and why? Step 1,

    asked by oscar on September 4, 2015
  2. 8th grade

    I am having trouble with these kinds of problems and I ask my teacher but he doesnt explain it good enough. Will you please tell me step by step instructions to solve this type of problem... -2(z + 11)=6 thank you

    asked by Sara on September 23, 2008
  3. Discrete Mathematics and its Application

    Am not understanding , how to do the truth or Venn diagram to show a statement pv(q^r)is equivalent to (pvq)^(pvr). How can I show the statement is not equivalent to (pvq)^r. I have to explain my answer in truth or Venn diagram,

    asked by Monique on August 9, 2016
  4. Chemistry

    I have to solve this combustion problem using Dimensional Analysis and molar heat: 2 C2H6 +7O2 yields 4 CO2 + 6H2O + 3120 kJ The question is to discover how much heat is produced along with 8 moles of water in this reaction. My

    asked by Narasaq on June 3, 2009
  5. Calculus

    Can someone show me a step by step process, along with explanations on how to do this problem? Thank you. :) Evaluate the integral ∫ [(x^2 - 1)/(x^2 + 1)]dx?

    asked by Aria on February 9, 2015

You can view more similar questions or ask a new question.