Sr Examen
Integral de 1/((2x-3)(2x+1)) dx
Solución
Ha introducido
[src]
m / | | 1 | ------------------- dx | (2*x - 3)*(2*x + 1) | / 0
$$\int\limits_{0}^{m} \frac{1}{\left(2 x - 3\right) \left(2 x + 1\right)}\, dx$$
Integral(1/((2*x - 3)*(2*x + 1)), (x, 0, m))
Respuesta (Indefinida)
[src]
/ | | 1 log(1 + 2*x) log(-3 + 2*x) | ------------------- dx = C - ------------ + ------------- | (2*x - 3)*(2*x + 1) 8 8 | /
$$\int \frac{1}{\left(2 x - 3\right) \left(2 x + 1\right)}\, dx = C + \frac{\log{\left(2 x - 3 \right)}}{8} - \frac{\log{\left(2 x + 1 \right)}}{8}$$
Respuesta
[src]
log(2) log(3/2) log(1/2 + m) log(-3/2 + m) pi*I
- ------ - -------- - ------------ + ------------- - ----
8 8 8 8 8
$$\frac{\log{\left(m - \frac{3}{2} \right)}}{8} - \frac{\log{\left(m + \frac{1}{2} \right)}}{8} - \frac{\log{\left(2 \right)}}{8} - \frac{\log{\left(\frac{3}{2} \right)}}{8} - \frac{i \pi}{8}$$
=
=
log(2) log(3/2) log(1/2 + m) log(-3/2 + m) pi*I
- ------ - -------- - ------------ + ------------- - ----
8 8 8 8 8
$$\frac{\log{\left(m - \frac{3}{2} \right)}}{8} - \frac{\log{\left(m + \frac{1}{2} \right)}}{8} - \frac{\log{\left(2 \right)}}{8} - \frac{\log{\left(\frac{3}{2} \right)}}{8} - \frac{i \pi}{8}$$
-log(2)/8 - log(3/2)/8 - log(1/2 + m)/8 + log(-3/2 + m)/8 - pi*i/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.