Sr Examen
Integral de ln((3x-1)/(5x+2)) dx
Solución
Ha introducido
[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))
Respuesta (Indefinida)
[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/ | /
$$\int \log{\left(\frac{3 x - 1}{5 x + 2} \right)}\, dx = C + x \log{\left(\frac{3 x - 1}{5 x + 2} \right)} - \frac{\log{\left(3 x - 1 \right)}}{3} - \frac{2 \log{\left(5 x + 2 \right)}}{5}$$
Gráfica
Respuesta
[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)
Respuesta numérica
[src]
(-2.01758394978084 + 1.02998797848403j)
(-2.01758394978084 + 1.02998797848403j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.