Sr Examen
Integral de (1/((2x+3)ln(x+9)^2)) dx
Solución
Ha introducido
[src]
oo / | | 1 | --------------------- dx | 2 | (2*x + 3)*log (x + 9) | / 1
$$\int\limits_{1}^{\infty} \frac{1}{\left(2 x + 3\right) \log{\left(x + 9 \right)}^{2}}\, dx$$
Integral(1/((2*x + 3)*log(x + 9)^2), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ / | | | 1 | 1 -9 - x | --------------------- dx = C - 15* | ------------------------------------------------ dx + -------------------- | 2 | 2 (3 + 2*x)*log(9 + x) | (2*x + 3)*log (x + 9) | 9*log(9 + x) + 4*x *log(9 + x) + 12*x*log(9 + x) | | / /
$$\int \frac{1}{\left(2 x + 3\right) \log{\left(x + 9 \right)}^{2}}\, dx = C + \frac{- x - 9}{\left(2 x + 3\right) \log{\left(x + 9 \right)}} - 15 \int \frac{1}{4 x^{2} \log{\left(x + 9 \right)} + 12 x \log{\left(x + 9 \right)} + 9 \log{\left(x + 9 \right)}}\, dx$$
Respuesta
[src]
oo
/
|
| 1 2
- 15* | ------------------------------------------------ dx + -------
| 2 log(10)
| 9*log(9 + x) + 4*x *log(9 + x) + 12*x*log(9 + x)
|
/
1
$$- 15 \int\limits_{1}^{\infty} \frac{1}{4 x^{2} \log{\left(x + 9 \right)} + 12 x \log{\left(x + 9 \right)} + 9 \log{\left(x + 9 \right)}}\, dx + \frac{2}{\log{\left(10 \right)}}$$
=
=
oo
/
|
| 1 2
- 15* | ------------------------------------------------ dx + -------
| 2 log(10)
| 9*log(9 + x) + 4*x *log(9 + x) + 12*x*log(9 + x)
|
/
1
$$- 15 \int\limits_{1}^{\infty} \frac{1}{4 x^{2} \log{\left(x + 9 \right)} + 12 x \log{\left(x + 9 \right)} + 9 \log{\left(x + 9 \right)}}\, dx + \frac{2}{\log{\left(10 \right)}}$$
-15*Integral(1/(9*log(9 + x) + 4*x^2*log(9 + x) + 12*x*log(9 + x)), (x, 1, oo)) + 2/log(10)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.