Sr Examen
Integral de dx/(x+sqrt2x-1) dx
Solución
Ha introducido
[src]
1 / | | 1 | --------------- dx | _____ | x + \/ 2*x - 1 | / 5
$$\int\limits_{5}^{1} \frac{1}{\left(x + \sqrt{2 x}\right) - 1}\, dx$$
Integral(1/(x + sqrt(2*x) - 1), (x, 5, 1))
Gráfica
Respuesta
[src]
/ ___ ___\ / ___ ___\ / ___ ___\ / ___ ___\
___ | \/ 2 \/ 6 | ___ | ___ \/ 2 \/ 6 | ___ | \/ 2 \/ 6 | ___ | ___ \/ 2 \/ 6 |
/ ___ ___\ / ___ ___\ \/ 3 *log|1 + ----- - -----| \/ 3 *log|\/ 5 + ----- + -----| \/ 3 *log|1 + ----- + -----| \/ 3 *log|\/ 5 + ----- - -----| / ___ ___\ / ___ ___\
| ___ \/ 2 \/ 6 | | ___ \/ 2 \/ 6 | \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / | \/ 2 \/ 6 | | \/ 2 \/ 6 |
- log|\/ 5 + ----- + -----| - log|\/ 5 + ----- - -----| - ---------------------------- - -------------------------------- + ---------------------------- + -------------------------------- + log|1 + ----- + -----| + log|1 + ----- - -----|
\ 2 2 / \ 2 2 / 3 3 3 3 \ 2 2 / \ 2 2 /
$$- \log{\left(\frac{\sqrt{2}}{2} + \frac{\sqrt{6}}{2} + \sqrt{5} \right)} - \frac{\sqrt{3} \log{\left(\frac{\sqrt{2}}{2} + \frac{\sqrt{6}}{2} + \sqrt{5} \right)}}{3} + \log{\left(- \frac{\sqrt{6}}{2} + \frac{\sqrt{2}}{2} + 1 \right)} - \log{\left(- \frac{\sqrt{6}}{2} + \frac{\sqrt{2}}{2} + \sqrt{5} \right)} + \frac{\sqrt{3} \log{\left(- \frac{\sqrt{6}}{2} + \frac{\sqrt{2}}{2} + \sqrt{5} \right)}}{3} - \frac{\sqrt{3} \log{\left(- \frac{\sqrt{6}}{2} + \frac{\sqrt{2}}{2} + 1 \right)}}{3} + \frac{\sqrt{3} \log{\left(\frac{\sqrt{2}}{2} + 1 + \frac{\sqrt{6}}{2} \right)}}{3} + \log{\left(\frac{\sqrt{2}}{2} + 1 + \frac{\sqrt{6}}{2} \right)}$$
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/ ___ ___\ / ___ ___\ / ___ ___\ / ___ ___\
___ | \/ 2 \/ 6 | ___ | ___ \/ 2 \/ 6 | ___ | \/ 2 \/ 6 | ___ | ___ \/ 2 \/ 6 |
/ ___ ___\ / ___ ___\ \/ 3 *log|1 + ----- - -----| \/ 3 *log|\/ 5 + ----- + -----| \/ 3 *log|1 + ----- + -----| \/ 3 *log|\/ 5 + ----- - -----| / ___ ___\ / ___ ___\
| ___ \/ 2 \/ 6 | | ___ \/ 2 \/ 6 | \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / | \/ 2 \/ 6 | | \/ 2 \/ 6 |
- log|\/ 5 + ----- + -----| - log|\/ 5 + ----- - -----| - ---------------------------- - -------------------------------- + ---------------------------- + -------------------------------- + log|1 + ----- + -----| + log|1 + ----- - -----|
\ 2 2 / \ 2 2 / 3 3 3 3 \ 2 2 / \ 2 2 /
$$- \log{\left(\frac{\sqrt{2}}{2} + \frac{\sqrt{6}}{2} + \sqrt{5} \right)} - \frac{\sqrt{3} \log{\left(\frac{\sqrt{2}}{2} + \frac{\sqrt{6}}{2} + \sqrt{5} \right)}}{3} + \log{\left(- \frac{\sqrt{6}}{2} + \frac{\sqrt{2}}{2} + 1 \right)} - \log{\left(- \frac{\sqrt{6}}{2} + \frac{\sqrt{2}}{2} + \sqrt{5} \right)} + \frac{\sqrt{3} \log{\left(- \frac{\sqrt{6}}{2} + \frac{\sqrt{2}}{2} + \sqrt{5} \right)}}{3} - \frac{\sqrt{3} \log{\left(- \frac{\sqrt{6}}{2} + \frac{\sqrt{2}}{2} + 1 \right)}}{3} + \frac{\sqrt{3} \log{\left(\frac{\sqrt{2}}{2} + 1 + \frac{\sqrt{6}}{2} \right)}}{3} + \log{\left(\frac{\sqrt{2}}{2} + 1 + \frac{\sqrt{6}}{2} \right)}$$
-log(sqrt(5) + sqrt(2)/2 + sqrt(6)/2) - log(sqrt(5) + sqrt(2)/2 - sqrt(6)/2) - sqrt(3)*log(1 + sqrt(2)/2 - sqrt(6)/2)/3 - sqrt(3)*log(sqrt(5) + sqrt(2)/2 + sqrt(6)/2)/3 + sqrt(3)*log(1 + sqrt(2)/2 + sqrt(6)/2)/3 + sqrt(3)*log(sqrt(5) + sqrt(2)/2 - sqrt(6)/2)/3 + log(1 + sqrt(2)/2 + sqrt(6)/2) + log(1 + sqrt(2)/2 - sqrt(6)/2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.