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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of cosx^2
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Integral of sinh(x)
- Integral of xcos(nx)
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Integral of arcsinx+arccosx
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Identical expressions
- 2x/((x- one)*(x²-x+ one))
- 2x divide by ((x minus 1) multiply by (x² minus x plus 1))
- 2x divide by ((x minus one) multiply by (x² minus x plus one))
- 2x/((x-1)(x²-x+1))
- 2x/x-1x²-x+1
- 2x divide by ((x-1)*(x²-x+1))
- 2x/((x-1)*(x²-x+1))dx
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Similar expressions
- 2x/((x+1)*(x²-x+1))
- 2x/((x-1)*(x²-x-1))
- 2x/((x-1)*(x²+x+1))
Integral of 2x/((x-1)*(x²-x+1)) dx
The solution
You have entered
[src]
1 / | | 2*x | -------------------- dx | / 2 \ | (x - 1)*\x - x + 1/ | / 0
$$\int\limits_{0}^{1} \frac{2 x}{\left(x - 1\right) \left(\left(x^{2} - x\right) + 1\right)}\, dx$$
Integral((2*x)/(((x - 1)*(x^2 - x + 1))), (x, 0, 1))
The answer (Indefinite)
[src]
/ ___ \ / ___ |2*\/ 3 *(-1/2 + x)| | 2*\/ 3 *atan|------------------| | 2*x / 2 \ \ 3 / | -------------------- dx = C - log\1 + x - x/ + 2*log(-1 + x) + -------------------------------- | / 2 \ 3 | (x - 1)*\x - x + 1/ | /
$$\int \frac{2 x}{\left(x - 1\right) \left(\left(x^{2} - x\right) + 1\right)}\, dx = C + 2 \log{\left(x - 1 \right)} - \log{\left(x^{2} - x + 1 \right)} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x - \frac{1}{2}\right)}{3} \right)}}{3}$$
The graph
The answer
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-oo - 2*pi*I
$$-\infty - 2 i \pi$$
=
=
-oo - 2*pi*I
$$-\infty - 2 i \pi$$
-oo - 2*pi*i
Use the examples entering the upper and lower limits of integration.