Sr Examen
Integral de (x^3-6)/(x^4+6x^2+8) dx
Solución
Ha introducido
[src]
1 / | | 3 | x - 6 | ------------- dx | 4 2 | x + 6*x + 8 | / 0
$$\int\limits_{0}^{1} \frac{x^{3} - 6}{\left(x^{4} + 6 x^{2}\right) + 8}\, dx$$
Integral((x^3 - 6)/(x^4 + 6*x^2 + 8), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ___\ | /x\ ___ |x*\/ 2 | | 3 / 2\ 3*atan|-| 3*\/ 2 *atan|-------| | x - 6 log\2 + x / \2/ \ 2 / / 2\ | ------------- dx = C - ----------- + --------- - --------------------- + log\4 + x / | 4 2 2 2 2 | x + 6*x + 8 | /
$$\int \frac{x^{3} - 6}{\left(x^{4} + 6 x^{2}\right) + 8}\, dx = C - \frac{\log{\left(x^{2} + 2 \right)}}{2} + \log{\left(x^{2} + 4 \right)} + \frac{3 \operatorname{atan}{\left(\frac{x}{2} \right)}}{2} - \frac{3 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}$$
Gráfica
Respuesta
[src]
/ ___\
___ |\/ 2 |
3*\/ 2 *atan|-----|
log(2) log(3) 3*atan(1/2) \ 2 /
------ - log(4) - ------ + ----------- - ------------------- + log(5)
2 2 2 2
$$- \log{\left(4 \right)} - \frac{3 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} - \frac{\log{\left(3 \right)}}{2} + \frac{\log{\left(2 \right)}}{2} + \frac{3 \operatorname{atan}{\left(\frac{1}{2} \right)}}{2} + \log{\left(5 \right)}$$
=
=
/ ___\
___ |\/ 2 |
3*\/ 2 *atan|-----|
log(2) log(3) 3*atan(1/2) \ 2 /
------ - log(4) - ------ + ----------- - ------------------- + log(5)
2 2 2 2
$$- \log{\left(4 \right)} - \frac{3 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} - \frac{\log{\left(3 \right)}}{2} + \frac{\log{\left(2 \right)}}{2} + \frac{3 \operatorname{atan}{\left(\frac{1}{2} \right)}}{2} + \log{\left(5 \right)}$$
log(2)/2 - log(4) - log(3)/2 + 3*atan(1/2)/2 - 3*sqrt(2)*atan(sqrt(2)/2)/2 + log(5)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.