Integral of (1/x+2/(x-1))dx dx
The solution
Detail solution
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Integrate term-by-term:
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The integral of a constant times a function is the constant times the integral of the function:
∫x−12dx=2∫x−11dx
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Let u=x−1.
Then let du=dx and substitute du:
∫u1du
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The integral of u1 is log(u).
Now substitute u back in:
log(x−1)
So, the result is: 2log(x−1)
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The integral of x1 is log(x).
The result is: log(x)+2log(x−1)
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Now simplify:
log(x)+2log(x−1)
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Add the constant of integration:
log(x)+2log(x−1)+constant
The answer is:
log(x)+2log(x−1)+constant
The answer (Indefinite)
[src]
/
|
| /1 2 \
| |- + -----| dx = C + 2*log(x - 1) + log(x)
| \x x - 1/
|
/
∫(x−12+x1)dx=C+log(x)+2log(x−1)
The graph
Use the examples entering the upper and lower limits of integration.