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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of e^x/x^2
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Integral of (1+x)/x
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Integral of coshx
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Integral of e^x/(e^(2*x)+1)
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Identical expressions
- (5x- one)/(two x^2-x- seven)
- (5x minus 1) divide by (2x squared minus x minus 7)
- (5x minus one) divide by (two x squared minus x minus seven)
- (5x-1)/(2x2-x-7)
- 5x-1/2x2-x-7
- (5x-1)/(2x²-x-7)
- (5x-1)/(2x to the power of 2-x-7)
- 5x-1/2x^2-x-7
- (5x-1) divide by (2x^2-x-7)
- (5x-1)/(2x^2-x-7)dx
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Similar expressions
- (5x+1)/(2x^2-x-7)
- (5x-1)/(2x^2+x-7)
- (5x-1)/(2x^2-x+7)
Integral of (5x-1)/(2x^2-x-7) dx
The solution
You have entered
[src]
1 / | | 5*x - 1 | ------------ dx | 2 | 2*x - x - 7 | / 0
$$\int\limits_{0}^{1} \frac{5 x - 1}{2 x^{2} - x - 7}\, dx$$
Integral((5*x - 1*1)/(2*x^2 - x - 1*7), (x, 0, 1))
The answer (Indefinite)
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/ / ____\ / ____\\ / ____ | | 1 \/ 57 | | 1 \/ 57 || | / 2\ \/ 57 *|- log|- - + x + ------| + log|- - + x - ------|| | 5*x - 1 5*log\-7 - x + 2*x / \ \ 4 4 / \ 4 4 // | ------------ dx = C + -------------------- + -------------------------------------------------------- | 2 4 228 | 2*x - x - 7 | /
$${{\log \left({{4\,x-\sqrt{57}-1}\over{4\,x+\sqrt{57}-1}}\right)
}\over{4\,\sqrt{57}}}+{{5\,\log \left(2\,x^2-x-7\right)}\over{4}}$$
The graph
The answer
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/ ____\ / ____\ / ____\ / / ____\\ / ____\ / ____\ / ____\ / / ____\\ |5 \/ 57 | |3 \/ 57 | |5 \/ 57 | | | 3 \/ 57 || |5 \/ 57 | | 1 \/ 57 | |5 \/ 57 | | |1 \/ 57 || |- - ------|*log|- + ------| + |- + ------|*|pi*I + log|- - + ------|| - |- - ------|*log|- - + ------| - |- + ------|*|pi*I + log|- + ------|| \4 228 / \4 4 / \4 228 / \ \ 4 4 // \4 228 / \ 4 4 / \4 228 / \ \4 4 //
$$-{{\log \left({{\sqrt{57}+29}\over{28}}\right)}\over{4\,\sqrt{57}}}
+{{\log \left(-{{\sqrt{57}-11}\over{8}}\right)}\over{4\,\sqrt{57}}}-
{{5\,\log 7}\over{4}}+{{5\,\log 6}\over{4}}$$
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/ ____\ / ____\ / ____\ / / ____\\ / ____\ / ____\ / ____\ / / ____\\ |5 \/ 57 | |3 \/ 57 | |5 \/ 57 | | | 3 \/ 57 || |5 \/ 57 | | 1 \/ 57 | |5 \/ 57 | | |1 \/ 57 || |- - ------|*log|- + ------| + |- + ------|*|pi*I + log|- - + ------|| - |- - ------|*log|- - + ------| - |- + ------|*|pi*I + log|- + ------|| \4 228 / \4 4 / \4 228 / \ \ 4 4 // \4 228 / \ 4 4 / \4 228 / \ \4 4 //
$$- \left(- \frac{\sqrt{57}}{228} + \frac{5}{4}\right) \log{\left(- \frac{1}{4} + \frac{\sqrt{57}}{4} \right)} + \left(- \frac{\sqrt{57}}{228} + \frac{5}{4}\right) \log{\left(\frac{3}{4} + \frac{\sqrt{57}}{4} \right)} - \left(\frac{\sqrt{57}}{228} + \frac{5}{4}\right) \left(\log{\left(\frac{1}{4} + \frac{\sqrt{57}}{4} \right)} + i \pi\right) + \left(\frac{\sqrt{57}}{228} + \frac{5}{4}\right) \left(\log{\left(- \frac{3}{4} + \frac{\sqrt{57}}{4} \right)} + i \pi\right)$$
The graph
Use the examples entering the upper and lower limits of integration.