In the given equation as follows, use partial fractions to find the indefinite i

iohanetc 2021-10-19 Answered
In the given equation as follows, use partial fractions to find the indefinite integral :-
see the equation as attached here
x2x22x+1dx
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Expert Answer

toroztatG
Answered 2021-10-20 Author has 98 answers
Step 1
We have to evaluate the following integral using partial fractions:
x2x22x+1dx
=(x22x+1+2x1x22x+1)dx
=(x22x+1x22x+1)dx+(2xx22x+1)dx(1x22x+1)dx
=dx+2xdx(x1)2dx(x1)2
=dx+[(x1)+(x1)(x1)2]dx+2dx(x1)2dx(x1)2
=dx+dxx1+dxx1+dx(x1)2
=dx+2dxx1+dx(x1)2
=x+2ln|x1|1x1+C
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