Evaluate the following integrals. int(dx)/(x^3-x^2)

Tazmin Horton 2021-01-06 Answered
Evaluate the following integrals.
dxx3x2
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Expert Answer

Jaylen Fountain
Answered 2021-01-07 Author has 170 answers
Step 1
Consider the provided integral,
dxx3x2
Evaluate the following integrals.
We can write as,
dxx3x2=1x2(x1)dx
First, we find the partial fraction.
1x2(x1)=a0x+a1x2+a3x1...(1)
Step 2
Now, multiply the equation by the provided denominator.
1x2(x1)x2(x1)=a0x2(x1)x+a1x2(x1)x2+a2x2(x1)x1
1=a0x(x1)+a1(x1)+a2x2
Compare the both the sides of the coefficient.
a1=1,a2=1
Using above values find the a0.
a0=1.
Step 3
Put the above values in the equation (1).
1x2(x1)=1x+1x2+1x1
=1x=1x2+1x1
So, the integrals becomes.
dxx3x2=1x2(x1)dx
=1xdx1x2dx+1x1dx
=ln|x|(1x)+ln|x1|
=ln|x|+1x+ln|x1|+C
Hence.
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