Sr Examen
Integral de sign(8-x)/(x^2+8*x+1) dx
Solución
Ha introducido
[src]
10 / | | sign(8 - x) | ------------ dx | 2 | x + 8*x + 1 | / 5
$$\int\limits_{5}^{10} \frac{\operatorname{sign}{\left(8 - x \right)}}{\left(x^{2} + 8 x\right) + 1}\, dx$$
Integral(sign(8 - x)/(x^2 + 8*x + 1), (x, 5, 10))
Respuesta (Indefinida)
[src]
/ / | | | sign(8 - x) | sign(8 - x) | ------------ dx = C + | ------------ dx | 2 | 2 | x + 8*x + 1 | 1 + x + 8*x | | / /
$$\int \frac{\operatorname{sign}{\left(8 - x \right)}}{\left(x^{2} + 8 x\right) + 1}\, dx = C + \int \frac{\operatorname{sign}{\left(8 - x \right)}}{x^{2} + 8 x + 1}\, dx$$
Respuesta
[src]
____ / ____\ ____ / ____\ ____ / ____\ ____ / ____\ ____ / ____\ ____ / ____\
\/ 15 *log\12 + \/ 15 / \/ 15 *log\9 - \/ 15 / \/ 15 *log\14 - \/ 15 / \/ 15 *log\12 - \/ 15 / \/ 15 *log\9 + \/ 15 / \/ 15 *log\14 + \/ 15 /
- ----------------------- - ---------------------- - ----------------------- + ----------------------- + ---------------------- + -----------------------
15 30 30 15 30 30
$$- \frac{\sqrt{15} \log{\left(\sqrt{15} + 12 \right)}}{15} - \frac{\sqrt{15} \log{\left(14 - \sqrt{15} \right)}}{30} - \frac{\sqrt{15} \log{\left(9 - \sqrt{15} \right)}}{30} + \frac{\sqrt{15} \log{\left(\sqrt{15} + 9 \right)}}{30} + \frac{\sqrt{15} \log{\left(\sqrt{15} + 14 \right)}}{30} + \frac{\sqrt{15} \log{\left(12 - \sqrt{15} \right)}}{15}$$
=
=
____ / ____\ ____ / ____\ ____ / ____\ ____ / ____\ ____ / ____\ ____ / ____\
\/ 15 *log\12 + \/ 15 / \/ 15 *log\9 - \/ 15 / \/ 15 *log\14 - \/ 15 / \/ 15 *log\12 - \/ 15 / \/ 15 *log\9 + \/ 15 / \/ 15 *log\14 + \/ 15 /
- ----------------------- - ---------------------- - ----------------------- + ----------------------- + ---------------------- + -----------------------
15 30 30 15 30 30
$$- \frac{\sqrt{15} \log{\left(\sqrt{15} + 12 \right)}}{15} - \frac{\sqrt{15} \log{\left(14 - \sqrt{15} \right)}}{30} - \frac{\sqrt{15} \log{\left(9 - \sqrt{15} \right)}}{30} + \frac{\sqrt{15} \log{\left(\sqrt{15} + 9 \right)}}{30} + \frac{\sqrt{15} \log{\left(\sqrt{15} + 14 \right)}}{30} + \frac{\sqrt{15} \log{\left(12 - \sqrt{15} \right)}}{15}$$
-sqrt(15)*log(12 + sqrt(15))/15 - sqrt(15)*log(9 - sqrt(15))/30 - sqrt(15)*log(14 - sqrt(15))/30 + sqrt(15)*log(12 - sqrt(15))/15 + sqrt(15)*log(9 + sqrt(15))/30 + sqrt(15)*log(14 + sqrt(15))/30
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.