Sr Examen
Integral de 1/(x*ln(3x+1)^2) dx
Solución
Ha introducido
[src]
oo / | | 1 | --------------- dx | 2 | x*log (3*x + 1) | / 2
$$\int\limits_{2}^{\infty} \frac{1}{x \log{\left(3 x + 1 \right)}^{2}}\, dx$$
Integral(1/(x*log(3*x + 1)^2), (x, 2, oo))
Respuesta (Indefinida)
[src]
/
|
| 1
| --------------- dx
| 2
/ | x *log(1 + 3*x)
| |
| 1 / -1 - 3*x
| --------------- dx = C - --------------------- + ----------------
| 2 3 3*x*log(1 + 3*x)
| x*log (3*x + 1)
|
/
$$\int \frac{1}{x \log{\left(3 x + 1 \right)}^{2}}\, dx = C - \frac{\int \frac{1}{x^{2} \log{\left(3 x + 1 \right)}}\, dx}{3} + \frac{- 3 x - 1}{3 x \log{\left(3 x + 1 \right)}}$$
Respuesta
[src]
oo
/
|
| 1
| --------------- dx
| 2
| x *log(1 + 3*x)
|
/
2 7
- ---------------------- + --------
3 6*log(7)
$$- \frac{\int\limits_{2}^{\infty} \frac{1}{x^{2} \log{\left(3 x + 1 \right)}}\, dx}{3} + \frac{7}{6 \log{\left(7 \right)}}$$
=
=
oo
/
|
| 1
| --------------- dx
| 2
| x *log(1 + 3*x)
|
/
2 7
- ---------------------- + --------
3 6*log(7)
$$- \frac{\int\limits_{2}^{\infty} \frac{1}{x^{2} \log{\left(3 x + 1 \right)}}\, dx}{3} + \frac{7}{6 \log{\left(7 \right)}}$$
-Integral(1/(x^2*log(1 + 3*x)), (x, 2, oo))/3 + 7/(6*log(7))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.