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