(2x^2-3x+8)dx/(2x^3-4x^2+8x-1)

2 years ago

Share

Answers : (1)

                    
Ans:
I = \int \frac{2x^{2}-3x+8}{2x^{3}-4x^{2}+8x-1}dx
We will proceed this question by partial fraction rule.
f(x) = 2x^{3}-4x^{2}+8x-1
Roots of f(x):
x_{1} = .1333
x_{2} = .93335+1.69707i
x_{3} = .93335-1.69707i
\frac{2x^{2}-3x+8}{2x^{3}-4x^{2}+8x-1} = \frac{a}{x-x_{1}} + \frac{b}{x-x_{2}}+\frac{c}{x-x_{3}}
We have values of a, b & c from here,
I = \int (\frac{a}{x-x_{1}}+\frac{b}{x-x_{2}}+\frac{c}{x-x_{3}})dx
I = aln|x-x_{1}| + bln|x-x_{2}| + cln|x-x_{3}| + constant
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty
22 days ago

Post Your Answer

More Questions On Integral Calculus

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
The value of the Integral Hint: p/2 (ax3 -p/2 cos x + b sin x + c)dx, depends on how many parameters among (a , b , c). Integral of an odd function over the interval [-a,a] is zero..
 
 
x^3 is odd--->0 sinx is odd--->0 only c will left in integration in integration, hence it depends only on c. Sher Mohammad B.Tech, IIT Delhi
  img
Sher Mohammad 4 months ago
 
x^3 is odd--->0 sinx is odd--->0 only c will left in integration in integration Sher Mohammad B.Tech, IIT Delhi
  img
Sher Mohammad 4 months ago
 
your question is not properly given
  img
MuraliKrishna Medavaram 4 months ago
a) Integrate 1/(1 - x^4) b) Integrate 1/(1 + x^4)
 
 
integrate the first one by partial fractions method... (1-x^4) = (1-x^2)(1+x^2) and proceed....
 
Varun Acharya 6 months ago
 
multiply numerator and denominator by 1- x^4 ... put x^4 = sinx
 
neeraj agarwal 6 months ago
What will be the anti derivative of e 3x ? Is there any method other than substitution to solve it?
 
 
Anti derivative of e 3x = ∫ e 3x dx = e 3x /3 + c I think substitution is the simplest way(substitute 3x for t) or just do it directly
 
Harikrishnan M B 13 days ago
Please suggest best book for preparing 3D for iit.
 
 
Dear tanayraj, Check the link below: http://www.askiitians.com/Important-books-iit-jee.aspx Cracking IIT just got more exciting,It s not just all about getting assistance from IITians,...
 
Aman Bansal one year ago
 
Arihant “Vectors and 3-D geometry”
 
Chetan Mandayam Nayakar one year ago
 
arihant parkashan,h.c.verma,r.d.sharma
 
Dilip chouhan one year ago
Differentiate y=Sin -1 (sqrt x X sqrt (1-x) + x X sqrt (1-x 2 )
 
 
Ans:
  img
Jitender Singh 4 days ago
A straight line makes an intercept on the y-axis twice as long as that on the x-axis and is at a unit distance from the origin. Determine its equation.
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 15 days ago
View all Questions »