Sr Examen
Integral de (2*ln(x)+8)/(4*sqrt(x-ln^2(x))) dx
Solución
Ha introducido
[src]
1 / | | 2*log(x) + 8 | ------------------ dx | _____________ | / 2 | 4*\/ x - log (x) | / 0
$$\int\limits_{0}^{1} \frac{2 \log{\left(x \right)} + 8}{4 \sqrt{x - \log{\left(x \right)}^{2}}}\, dx$$
Integral((2*log(x) + 8)/((4*sqrt(x - log(x)^2))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/
|
| log(x)
| ---------------- dx
| _____________
| / 2
/ | \/ x - log (x) /
| | |
| 2*log(x) + 8 / | 1
| ------------------ dx = C + ---------------------- + 2* | ---------------- dx
| _____________ 2 | _____________
| / 2 | / 2
| 4*\/ x - log (x) | \/ x - log (x)
| |
/ /
$$\int \frac{2 \log{\left(x \right)} + 8}{4 \sqrt{x - \log{\left(x \right)}^{2}}}\, dx = C + \frac{\int \frac{\log{\left(x \right)}}{\sqrt{x - \log{\left(x \right)}^{2}}}\, dx}{2} + 2 \int \frac{1}{\sqrt{x - \log{\left(x \right)}^{2}}}\, dx$$
Respuesta
[src]
1 1
/ /
| |
| 4 | log(x)
| ---------------- dx | ---------------- dx
| _____________ | _____________
| / 2 | / 2
| \/ x - log (x) | \/ x - log (x)
| |
/ /
0 0
----------------------- + -----------------------
2 2
$$\frac{\int\limits_{0}^{1} \frac{4}{\sqrt{x - \log{\left(x \right)}^{2}}}\, dx}{2} + \frac{\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{\sqrt{x - \log{\left(x \right)}^{2}}}\, dx}{2}$$
=
=
1 1
/ /
| |
| 4 | log(x)
| ---------------- dx | ---------------- dx
| _____________ | _____________
| / 2 | / 2
| \/ x - log (x) | \/ x - log (x)
| |
/ /
0 0
----------------------- + -----------------------
2 2
$$\frac{\int\limits_{0}^{1} \frac{4}{\sqrt{x - \log{\left(x \right)}^{2}}}\, dx}{2} + \frac{\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{\sqrt{x - \log{\left(x \right)}^{2}}}\, dx}{2}$$
Integral(4/sqrt(x - log(x)^2), (x, 0, 1))/2 + Integral(log(x)/sqrt(x - log(x)^2), (x, 0, 1))/2
Respuesta numérica
[src]
(1.44459267392123 - 0.766826528703993j)
(1.44459267392123 - 0.766826528703993j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.