(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
29 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
find the length of the curve y=(1/3)(x^2+2)^3/2 ?
 
 
Length : root ( dy^2 + dx^2) and then its integral.. dL = dx * root (dy/dx^2 + 1) dL = dx * root ( x^4 + 2x^2 + 1) dL = dx * (x^2 + 1) Integrate it and now put the limits. This is the answer...
  img
bharat bajaj 4 months ago
If f (x) = x2 1/x2 v sin( t)dt, then find the value of f (1).
 
 
please specify the question clearly so that it is understandable Thanks & Regards Parvez Ali askIITians Faculty
  img
Parvez ali 4 months ago
 
Thanks & Regards, Nirmal Singh Askiitians Faculty
  img
Nirmal Singh. 4 months ago
 
please specify the question clearly
  img
Parvez ali 4 months ago
Find the area of the region between the curves y=x²+x and the x-axis on the interval closed interval 1,4 using limit of riemannn sums
 
 
area under the curve is always =S(y)dx where S is the sign of integral.. hence.. area under the above curve would be =S(x²+x)dx =S(x²)dx+S(x)dx =(x^3)/3+(x^2)/2+c.... we can do the above by...
 
Harsh davda 4 months ago
show that of all the rectangles inscribed in a fixed circle ,the square has the maximum area
 
 
Hello Student, Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar 23 days ago
how to draw vector triangle?
 
 
Suppose 2 vectors A and B are to be added according to the triangle law of vector addition . Let us draw these two vectors. OA vector=A vector and AB vector=B vector. First draw a right...
 
Kurma Anudeep 2 years ago
 
For vector triangle. Take two vectors with co initial points. then join their other side together to get the resultant. eg. AB and BC be two vectors meeting at B. then resultant will be AC
 
G Ashwin - one year ago
View all Questions »