Calculus AB

Please help me integrate this equation using partial fractions:

Integrate [(x^2+5)/(x^3-x^2+x+3)]dx.

Thank you very much.

  1. 👍 0
  2. 👎 0
  3. 👁 108
  1. x^3-x^2+x+3=(x+1)(x^2-2x+3)

    (x^2+5)/(x^3-x^2+x+3)=
    =A/(x+1)+(Bx+C)/(x^2-2x+3)

    A(x^2-2x+3)+(Bx+C)(x+1)=x^2+5

    A+B=1
    -2A+B+C=0
    3A+C=5
    Find A,B,C

    1. 👍 0
    2. 👎 0
  2. In google type:
    wolfram alpha

    When you see list of results click on:
    Wolfram Alpha:Computational Knoweledge Engine

    When page be open in rectangle type:
    (x^2+5)/(x^3-x^2+x+3) and click option =

    After few secons you will see all about that function.

    Now click option:
    Partial fraction expansion: Show steps

    Now in wolfram alpha rectangle type:
    2/(x^2-2x+3)+1/(x+1)
    and click option =

    When you see results clic option:
    Indefinite integral: Show steps

    1. 👍 0
    2. 👎 0
  3. Thank you very much.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math, calculus 2

    Consider the area between the graphs x+y=16 and x+4= (y^2). This area can be computed in two different ways using integrals. First of all it can be computed as a sum of two integrals integrate from a to b of f(x)dx + integrate

    asked by bobby on September 12, 2012
  2. Business

    Your CEO is concerned that too much productivity is lost by having employees call each other, only to be directed to voice mail. He asks you if something can be done to counter this. What do you suggest? a) Integrate Dropbox into

    asked by Amber on August 31, 2019
  3. Math

    find the volume bounded by the parabolic cylinder z=4-x^2 and the planes x=0, y=0, y=6 and z=0 I just want some help figuring out the limits of this question : So for z, we have to integrate from z=0 to z=4-x^2 (am i right?)

    asked by Aryaa on October 19, 2019
  4. Calculus

    Sketch the regions enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. integrate with either respect to x or y, then find area S

    asked by saywhat on October 21, 2010
  1. calculus

    1) Integrate Cos^n(x) dx 2) Integrate e^(ax)Sinbx dx 3) Integrate (5xCos3x) dx I Will be happy to critique your thinking on these. 1) Derive a recursive relation. 2) Simplest by replacing sin(bx) by Exp[i b x] and taking imaginary

    asked by Febby on April 13, 2007
  2. Mathematics-Integration

    Question: Prove that [integrate {x*sin2x*sin[π/2*cos x]} dx] /(2x-π) } from (0-π) = [ integrate {sin x*cos x*sin[π/2*cos x} dx ] from (0-π). My thoughts on the question: We know that integrate f(x) dx from (0-a) = integrate

    asked by Shenaya on June 8, 2017
  3. Math Integration

    Integrate: f (x)/(2x + 1) dx let f represent integrate sign let u = x, du = dx => dx = du = f (u)/(2u + 1) du = f u (2u + 1)^(-1) du = (1/2)u^2 (ln|2u + 1|) + c = (1/2)x^2 (ln|2x + 1|) + c ...what did I do wrong? The correct

    asked by Anonymous on February 11, 2009
  4. Calculus

    How do you integrate [(x^2)(cos(2(x^3)))]? I tried to integrate by parts but I'm going in circles yet again...

    asked by Hannah on February 13, 2009
  1. Calculus

    dy/dx = 4ye^(5x) a) Separate the differential equation, then integrate both sides. b) Write the general solution as a function y(x). For the second part, I got y(x)=e^((5e^(5x))/(5)) + C but I don't understand how to separate

    asked by Jamie on June 16, 2014
  2. physics (mechanics)

    Practice problem: A rocket sled for testing equipment under large accelerations starts at rest and accelerates according to the expression: a= (2.8 m/s^3)t + (3.9 m/s^2) How far does the rocket move in the time interval t=0 to

    asked by John on August 28, 2010
  3. Calculus

    Which of the following choices will most easily evaluate the integral of [L(x)]/[P(x)] dx, where L(x) is a logarithmic function and P(x) is a polynomial? a) Integrate the polynomial function and differentiate the logarithmic

    asked by Alice on March 22, 2019
  4. Calculus

    Could someone explain how do we verify stokes theorem for the vector field F=zi + (2x+z)j + xk taken over the triangular surface S in the plane (x/1)+(y/2)+(z/3)=1 bounded by the planes x=0 y=0 and z=0. Take boundary of the above

    asked by Aryaa on November 23, 2019

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