+91-87964 74404
FlagBACK
Question icon
Integral Calculus

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

Profile image of Mayank Gupta
14 Years agoGrade
Answers icon

1 Answer

Profile image of Jitender Singh
12 Years ago
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

Other Related Questions on integral calculus

question mark
The area of a square field is 640000cm2.what is its area in hectares
integral calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
Please solve this integration. I am facing difficulty in it
 How to solve this. Please solve anyone. Humble request
integral calculus
1 Answer Available

Last Activity: 4 Years ago

question mark
Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0
integral calculus
1 Answer Available

Last Activity: 4 Years ago

question mark
If 4th term of an A.p is zero, show that the 8th term is double the 6th term
 
integral calculus
1 Answer Available

Last Activity: 4 Years ago