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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^5dx
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Integral of x/(x^2+2x+2)
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Integral of x*exp(-4*x)
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Integral of 1/(x^2-2*x)
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Identical expressions
- dx/(2x- one)(2x+ three)
- dx divide by (2x minus 1)(2x plus 3)
- dx divide by (2x minus one)(2x plus three)
- dx/2x-12x+3
- dx divide by (2x-1)(2x+3)
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Similar expressions
- dx/(2x-1)(2x-3)
- dx/(2x+1)(2x+3)
Integral of dx/(2x-1)(2x+3) dx
The solution
You have entered
[src]
___ \/ 3 / | | 2*x + 3 | ------- dx | 2*x - 1 | / ___ \/ 3 ----- 3
$$\int\limits_{\frac{\sqrt{3}}{3}}^{\sqrt{3}} \frac{2 x + 3}{2 x - 1}\, dx$$
Integral((2*x + 3)/(2*x - 1), (x, sqrt(3)/3, sqrt(3)))
The answer (Indefinite)
[src]
/ | | 2*x + 3 | ------- dx = C + x + 2*log(-1 + 2*x) | 2*x - 1 | /
$$\int \frac{2 x + 3}{2 x - 1}\, dx = C + x + 2 \log{\left(2 x - 1 \right)}$$
The graph
The answer
[src]
/ ___\ ___
| 2*\/ 3 | / ___\ 2*\/ 3
- 2*log|-1 + -------| + 2*log\-1 + 2*\/ 3 / + -------
\ 3 / 3
$$\frac{2 \sqrt{3}}{3} + 2 \log{\left(-1 + 2 \sqrt{3} \right)} - 2 \log{\left(-1 + \frac{2 \sqrt{3}}{3} \right)}$$
=
=
/ ___\ ___
| 2*\/ 3 | / ___\ 2*\/ 3
- 2*log|-1 + -------| + 2*log\-1 + 2*\/ 3 / + -------
\ 3 / 3
$$\frac{2 \sqrt{3}}{3} + 2 \log{\left(-1 + 2 \sqrt{3} \right)} - 2 \log{\left(-1 + \frac{2 \sqrt{3}}{3} \right)}$$
-2*log(-1 + 2*sqrt(3)/3) + 2*log(-1 + 2*sqrt(3)) + 2*sqrt(3)/3
Use the examples entering the upper and lower limits of integration.