Sr Examen
Integral de x/((x+5)^2ln^2) dx
Solución
Ha introducido
[src]
oo / | | x | ---------------- dx | 2 2 | (x + 5) *log (x) | / 2
$$\int\limits_{2}^{\infty} \frac{x}{\left(x + 5\right)^{2} \log{\left(x \right)}^{2}}\, dx$$
Integral(x/(((x + 5)^2*log(x)^2)), (x, 2, oo))
Respuesta (Indefinida)
[src]
/ / | | 2 | x | x x | ---------------- dx = C + 10* | --------------------------------------------------- dx - ----------------------- | 2 2 | 3 2 / 2 \ | (x + 5) *log (x) | 125*log(x) + x *log(x) + 15*x *log(x) + 75*x*log(x) \25 + x + 10*x/*log(x) | | / /
$$\int \frac{x}{\left(x + 5\right)^{2} \log{\left(x \right)}^{2}}\, dx = C - \frac{x^{2}}{\left(x^{2} + 10 x + 25\right) \log{\left(x \right)}} + 10 \int \frac{x}{x^{3} \log{\left(x \right)} + 15 x^{2} \log{\left(x \right)} + 75 x \log{\left(x \right)} + 125 \log{\left(x \right)}}\, dx$$
Respuesta
[src]
oo
/
|
| x 4
10* | --------------------------------------------------- dx + ---------
| 3 2 49*log(2)
| 125*log(x) + x *log(x) + 15*x *log(x) + 75*x*log(x)
|
/
2
$$10 \int\limits_{2}^{\infty} \frac{x}{x^{3} \log{\left(x \right)} + 15 x^{2} \log{\left(x \right)} + 75 x \log{\left(x \right)} + 125 \log{\left(x \right)}}\, dx + \frac{4}{49 \log{\left(2 \right)}}$$
=
=
oo
/
|
| x 4
10* | --------------------------------------------------- dx + ---------
| 3 2 49*log(2)
| 125*log(x) + x *log(x) + 15*x *log(x) + 75*x*log(x)
|
/
2
$$10 \int\limits_{2}^{\infty} \frac{x}{x^{3} \log{\left(x \right)} + 15 x^{2} \log{\left(x \right)} + 75 x \log{\left(x \right)} + 125 \log{\left(x \right)}}\, dx + \frac{4}{49 \log{\left(2 \right)}}$$
10*Integral(x/(125*log(x) + x^3*log(x) + 15*x^2*log(x) + 75*x*log(x)), (x, 2, oo)) + 4/(49*log(2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.