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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 1/sqrt(1+u^2)
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Integral of (2x+3)
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Integral of 1-7*x^2
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Integral of (x-1)/x^3
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Identical expressions
- (3x- one)/(x^ two +10x+ six)
- (3x minus 1) divide by (x squared plus 10x plus 6)
- (3x minus one) divide by (x to the power of two plus 10x plus six)
- (3x-1)/(x2+10x+6)
- 3x-1/x2+10x+6
- (3x-1)/(x²+10x+6)
- (3x-1)/(x to the power of 2+10x+6)
- 3x-1/x^2+10x+6
- (3x-1) divide by (x^2+10x+6)
- (3x-1)/(x^2+10x+6)dx
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Similar expressions
- (3x+1)/(x^2+10x+6)
- (3x-1)/(x^2-10x+6)
- (3x-1)/(x^2+10x-6)
Integral of (3x-1)/(x^2+10x+6) dx
The solution
You have entered
[src]
1 / | | 3*x - 1 | ------------- dx | 2 | x + 10*x + 6 | / 0
$$\int\limits_{0}^{1} \frac{3 x - 1}{x^{2} + 10 x + 6}\, dx$$
Integral((3*x - 1*1)/(x^2 + 10*x + 6), (x, 0, 1))
The answer (Indefinite)
[src]
/ | / 2 \ ____ / / ____\ / ____\\ | 3*x - 1 3*log\6 + x + 10*x/ 8*\/ 19 *\- log\5 + x + \/ 19 / + log\5 + x - \/ 19 // | ------------- dx = C + -------------------- - ------------------------------------------------------ | 2 2 19 | x + 10*x + 6 | /
$${{3\,\log \left(x^2+10\,x+6\right)}\over{2}}-{{8\,\log \left({{2\,x
-2\,\sqrt{19}+10}\over{2\,x+2\,\sqrt{19}+10}}\right)}\over{\sqrt{19}
}}$$
The graph
The answer
[src]
/ ____\ / ____\ / ____\ / ____\ |3 8*\/ 19 | / ____\ |3 8*\/ 19 | / ____\ |3 8*\/ 19 | / ____\ |3 8*\/ 19 | / ____\ |- - --------|*log\6 - \/ 19 / + |- + --------|*log\6 + \/ 19 / - |- - --------|*log\5 - \/ 19 / - |- + --------|*log\5 + \/ 19 / \2 19 / \2 19 / \2 19 / \2 19 /
$$-{{8\,\log \left(-{{12\,\sqrt{19}-55}\over{17}}\right)}\over{\sqrt{
19}}}+{{8\,\log \left(-{{5\,\sqrt{19}-22}\over{3}}\right)}\over{
\sqrt{19}}}+{{3\,\log 17}\over{2}}-{{3\,\log 6}\over{2}}$$
=
=
/ ____\ / ____\ / ____\ / ____\ |3 8*\/ 19 | / ____\ |3 8*\/ 19 | / ____\ |3 8*\/ 19 | / ____\ |3 8*\/ 19 | / ____\ |- - --------|*log\6 - \/ 19 / + |- + --------|*log\6 + \/ 19 / - |- - --------|*log\5 - \/ 19 / - |- + --------|*log\5 + \/ 19 / \2 19 / \2 19 / \2 19 / \2 19 /
$$- \left(\frac{3}{2} + \frac{8 \sqrt{19}}{19}\right) \log{\left(\sqrt{19} + 5 \right)} + \left(- \frac{8 \sqrt{19}}{19} + \frac{3}{2}\right) \log{\left(- \sqrt{19} + 6 \right)} - \left(- \frac{8 \sqrt{19}}{19} + \frac{3}{2}\right) \log{\left(- \sqrt{19} + 5 \right)} + \left(\frac{3}{2} + \frac{8 \sqrt{19}}{19}\right) \log{\left(\sqrt{19} + 6 \right)}$$
The graph
Use the examples entering the upper and lower limits of integration.