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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^(2*x+1)
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Integral of sin(5x)
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Integral of -xe^x
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Integral of x*dx/(x^2-1)
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Identical expressions
- ln((3x- one)/(5x+ two))
- ln((3x minus 1) divide by (5x plus 2))
- ln((3x minus one) divide by (5x plus two))
- ln3x-1/5x+2
- ln((3x-1) divide by (5x+2))
- ln((3x-1)/(5x+2))dx
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Similar expressions
- ln((3x+1)/(5x+2))
- ln((3x-1)/(5x-2))
Integral of ln((3x-1)/(5x+2)) dx
The solution
You have entered
[src]
1 / | | /3*x - 1\ | log|-------| dx | \5*x + 2/ | / 0
$$\int\limits_{0}^{1} \log{\left(\frac{3 x - 1}{5 x + 2} \right)}\, dx$$
Integral(log((3*x - 1)/(5*x + 2)), (x, 0, 1))
The answer (Indefinite)
[src]
/ | | /3*x - 1\ 2*log(2 + 5*x) log(-1 + 3*x) /3*x - 1\ | log|-------| dx = C - -------------- - ------------- + x*log|-------| | \5*x + 2/ 5 3 \5*x + 2/ | /
$$\int \log{\left(\frac{3 x - 1}{5 x + 2} \right)}\, dx = C + x \log{\left(\frac{3 x - 1}{5 x + 2} \right)} - \frac{\log{\left(3 x - 1 \right)}}{3} - \frac{2 \log{\left(5 x + 2 \right)}}{5}$$
The graph
The answer
[src]
2*log(7/5) log(3) log(2/3) 2*log(2/5) pi*I
- ---------- - ------ - -------- + ---------- + ---- + log(2/7)
5 3 3 5 3
$$\log{\left(\frac{2}{7} \right)} + \frac{2 \log{\left(\frac{2}{5} \right)}}{5} - \frac{\log{\left(3 \right)}}{3} - \frac{2 \log{\left(\frac{7}{5} \right)}}{5} - \frac{\log{\left(\frac{2}{3} \right)}}{3} + \frac{i \pi}{3}$$
=
=
2*log(7/5) log(3) log(2/3) 2*log(2/5) pi*I
- ---------- - ------ - -------- + ---------- + ---- + log(2/7)
5 3 3 5 3
$$\log{\left(\frac{2}{7} \right)} + \frac{2 \log{\left(\frac{2}{5} \right)}}{5} - \frac{\log{\left(3 \right)}}{3} - \frac{2 \log{\left(\frac{7}{5} \right)}}{5} - \frac{\log{\left(\frac{2}{3} \right)}}{3} + \frac{i \pi}{3}$$
-2*log(7/5)/5 - log(3)/3 - log(2/3)/3 + 2*log(2/5)/5 + pi*i/3 + log(2/7)
Numerical answer
[src]
(-2.01758394978084 + 1.02998797848403j)
(-2.01758394978084 + 1.02998797848403j)
Use the examples entering the upper and lower limits of integration.