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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x/(raiz(2x-5))
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Integral of (x+1)/(x^2+2x-1)
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Integral of (x+1)/(2x²+3x-4)
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Integral of e^ydy
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Identical expressions
- one ÷((x- one)*(x²+ one))
- 1÷((x minus 1) multiply by (x² plus 1))
- one ÷((x minus one) multiply by (x² plus one))
- 1÷((x-1)(x²+1))
- 1÷x-1x²+1
- 1÷((x-1)*(x²+1))dx
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Similar expressions
- 1÷((x+1)*(x²+1))
- 1÷((x-1)*(x²-1))
Integral of 1÷((x-1)*(x²+1)) dx
The solution
You have entered
[src]
1 / | | 1 | ---------------- dx | / 2 \ | (x - 1)*\x + 1/ | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x - 1\right) \left(x^{2} + 1\right)}\, dx$$
Integral(1/((x - 1)*(x^2 + 1)), (x, 0, 1))
The answer (Indefinite)
[src]
/ | / 2\ | 1 log(-1 + x) atan(x) log\1 + x / | ---------------- dx = C + ----------- - ------- - ----------- | / 2 \ 2 2 4 | (x - 1)*\x + 1/ | /
$$\int \frac{1}{\left(x - 1\right) \left(x^{2} + 1\right)}\, dx = C + \frac{\log{\left(x - 1 \right)}}{2} - \frac{\log{\left(x^{2} + 1 \right)}}{4} - \frac{\operatorname{atan}{\left(x \right)}}{2}$$
The graph
The answer
[src]
pi*I
-oo - ----
2
$$-\infty - \frac{i \pi}{2}$$
=
=
pi*I
-oo - ----
2
$$-\infty - \frac{i \pi}{2}$$
-oo - pi*i/2
Use the examples entering the upper and lower limits of integration.