Sr Examen
Integral de 1/((3x-5)(ln(4x-7))^2) dx
Solución
Ha introducido
[src]
oo / | | 1 | ----------------------- dx | 2 | (3*x - 5)*log (4*x - 7) | / 3
$$\int\limits_{3}^{\infty} \frac{1}{\left(3 x - 5\right) \log{\left(4 x - 7 \right)}^{2}}\, dx$$
Integral(1/((3*x - 5)*log(4*x - 7)^2), (x, 3, oo))
Respuesta (Indefinida)
[src]
/
|
| 1
| ---------------------------------------------------------- dx
| 2
/ | 25*log(-7 + 4*x) - 30*x*log(-7 + 4*x) + 9*x *log(-7 + 4*x)
| |
| 1 / 7 - 4*x
| ----------------------- dx = C + ---------------------------------------------------------------- + --------------------------
| 2 4 (-20 + 12*x)*log(-7 + 4*x)
| (3*x - 5)*log (4*x - 7)
|
/
$$\int \frac{1}{\left(3 x - 5\right) \log{\left(4 x - 7 \right)}^{2}}\, dx = C + \frac{7 - 4 x}{\left(12 x - 20\right) \log{\left(4 x - 7 \right)}} + \frac{\int \frac{1}{9 x^{2} \log{\left(4 x - 7 \right)} - 30 x \log{\left(4 x - 7 \right)} + 25 \log{\left(4 x - 7 \right)}}\, dx}{4}$$
Respuesta
[src]
oo
/
|
| 1
| ---------------------------------------------------------- dx
| 2
| 25*log(-7 + 4*x) - 30*x*log(-7 + 4*x) + 9*x *log(-7 + 4*x)
|
/
3 5
----------------------------------------------------------------- + ---------
4 16*log(5)
$$\frac{\int\limits_{3}^{\infty} \frac{1}{9 x^{2} \log{\left(4 x - 7 \right)} - 30 x \log{\left(4 x - 7 \right)} + 25 \log{\left(4 x - 7 \right)}}\, dx}{4} + \frac{5}{16 \log{\left(5 \right)}}$$
=
=
oo
/
|
| 1
| ---------------------------------------------------------- dx
| 2
| 25*log(-7 + 4*x) - 30*x*log(-7 + 4*x) + 9*x *log(-7 + 4*x)
|
/
3 5
----------------------------------------------------------------- + ---------
4 16*log(5)
$$\frac{\int\limits_{3}^{\infty} \frac{1}{9 x^{2} \log{\left(4 x - 7 \right)} - 30 x \log{\left(4 x - 7 \right)} + 25 \log{\left(4 x - 7 \right)}}\, dx}{4} + \frac{5}{16 \log{\left(5 \right)}}$$
Integral(1/(25*log(-7 + 4*x) - 30*x*log(-7 + 4*x) + 9*x^2*log(-7 + 4*x)), (x, 3, oo))/4 + 5/(16*log(5))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.