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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of (xe^x)dx
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Integral of (x+2)sin3x
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Integral of x^2*e^(x/2)*dx
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Integral of (x^2-6*x+4)/(x^2+2*x+4)
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Identical expressions
- (x*dx)/(one +x-x^ two)
- (x multiply by dx) divide by (1 plus x minus x squared )
- (x multiply by dx) divide by (one plus x minus x to the power of two)
- (x*dx)/(1+x-x2)
- x*dx/1+x-x2
- (x*dx)/(1+x-x²)
- (x*dx)/(1+x-x to the power of 2)
- (xdx)/(1+x-x^2)
- (xdx)/(1+x-x2)
- xdx/1+x-x2
- xdx/1+x-x^2
- (x*dx) divide by (1+x-x^2)
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Similar expressions
- (x*dx)/(1-x-x^2)
- (x*dx)/(1+x+x^2)
Integral of (x*dx)/(1+x-x^2) dx
The solution
You have entered
[src]
1 / | | 1 | x*1*---------- dx | 2 | 1 + x - x | / 0
$$\int\limits_{0}^{1} x 1 \cdot \frac{1}{- x^{2} + x + 1}\, dx$$
Integral(x*1/(1 + x - x^2), (x, 0, 1))
The answer (Indefinite)
[src]
/ / ___\ / ___\\ / ___ | | 1 \/ 5 | | 1 \/ 5 || | / 2\ \/ 5 *|- log|- - + x + -----| + log|- - + x - -----|| | 1 log\1 + x - x / \ \ 2 2 / \ 2 2 // | x*1*---------- dx = C - --------------- - ----------------------------------------------------- | 2 2 10 | 1 + x - x | /
$$-{{\log \left({{2\,x-\sqrt{5}-1}\over{2\,x+\sqrt{5}-1}}\right)
}\over{2\,\sqrt{5}}}-{{\log \left(x^2-x-1\right)}\over{2}}$$
The graph
The answer
[src]
/ ___\ / ___\ / ___\ / / ___\\ / ___\ / ___\ / ___\ / / ___\\ |1 \/ 5 | | 1 \/ 5 | |1 \/ 5 | | |1 \/ 5 || |1 \/ 5 | |1 \/ 5 | |1 \/ 5 | | | 1 \/ 5 || |- - -----|*log|- - + -----| + |- + -----|*|pi*I + log|- + -----|| - |- - -----|*log|- + -----| - |- + -----|*|pi*I + log|- - + -----|| \2 10 / \ 2 2 / \2 10 / \ \2 2 // \2 10 / \2 2 / \2 10 / \ \ 2 2 //
$${{\log \left({{\sqrt{5}+3}\over{2}}\right)}\over{2\,\sqrt{5}}}-{{
\log \left(-{{\sqrt{5}-3}\over{2}}\right)}\over{2\,\sqrt{5}}}$$
=
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/ ___\ / ___\ / ___\ / / ___\\ / ___\ / ___\ / ___\ / / ___\\ |1 \/ 5 | | 1 \/ 5 | |1 \/ 5 | | |1 \/ 5 || |1 \/ 5 | |1 \/ 5 | |1 \/ 5 | | | 1 \/ 5 || |- - -----|*log|- - + -----| + |- + -----|*|pi*I + log|- + -----|| - |- - -----|*log|- + -----| - |- + -----|*|pi*I + log|- - + -----|| \2 10 / \ 2 2 / \2 10 / \ \2 2 // \2 10 / \2 2 / \2 10 / \ \ 2 2 //
$$\left(- \frac{\sqrt{5}}{10} + \frac{1}{2}\right) \log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)} - \left(- \frac{\sqrt{5}}{10} + \frac{1}{2}\right) \log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} - \left(\frac{\sqrt{5}}{10} + \frac{1}{2}\right) \left(\log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + i \pi\right) + \left(\frac{\sqrt{5}}{10} + \frac{1}{2}\right) \left(\log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + i \pi\right)$$
The graph
Use the examples entering the upper and lower limits of integration.