Sr Examen
Integral de (2x-1)/(x^4+5x^2+6) dx
Solución
Ha introducido
[src]
1 / | | 2*x - 1 | ------------- dx | 4 2 | x + 5*x + 6 | / 0
$$\int\limits_{0}^{1} \frac{2 x - 1}{\left(x^{4} + 5 x^{2}\right) + 6}\, dx$$
Integral((2*x - 1)/(x^4 + 5*x^2 + 6), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___\ / ___\ / ___ |x*\/ 2 | ___ |x*\/ 3 | | \/ 2 *atan|-------| \/ 3 *atan|-------| | 2*x - 1 / 2\ \ 2 / \ 3 / / 2\ | ------------- dx = C - log\3 + x / - ------------------- + ------------------- + log\2 + x / | 4 2 2 3 | x + 5*x + 6 | /
$$\int \frac{2 x - 1}{\left(x^{4} + 5 x^{2}\right) + 6}\, dx = C + \log{\left(x^{2} + 2 \right)} - \log{\left(x^{2} + 3 \right)} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)}}{3}$$
Gráfica
Respuesta
[src]
/ ___\
___ |\/ 2 |
\/ 2 *atan|-----| ___
\ 2 / pi*\/ 3
-log(2) - log(4) + 2*log(3) - ----------------- + --------
2 18
$$- \log{\left(4 \right)} - \log{\left(2 \right)} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} + \frac{\sqrt{3} \pi}{18} + 2 \log{\left(3 \right)}$$
=
=
/ ___\
___ |\/ 2 |
\/ 2 *atan|-----| ___
\ 2 / pi*\/ 3
-log(2) - log(4) + 2*log(3) - ----------------- + --------
2 18
$$- \log{\left(4 \right)} - \log{\left(2 \right)} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} + \frac{\sqrt{3} \pi}{18} + 2 \log{\left(3 \right)}$$
-log(2) - log(4) + 2*log(3) - sqrt(2)*atan(sqrt(2)/2)/2 + pi*sqrt(3)/18
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.