Sr Examen
Integral de x/(x^4+12x^2+225) dx
Solución
Ha introducido
[src]
___ \/ 2 / | | x | ---------------- dx | 4 2 | x + 12*x + 225 | / 0
$$\int\limits_{0}^{\sqrt{2}} \frac{x}{\left(x^{4} + 12 x^{2}\right) + 225}\, dx$$
Integral(x/(x^4 + 12*x^2 + 225), (x, 0, sqrt(2)))
Respuesta (Indefinida)
[src]
/ ____ / 2\\ / ____ |\/ 21 *\6 + x /| | \/ 21 *atan|---------------| | x \ 63 / | ---------------- dx = C + ---------------------------- | 4 2 126 | x + 12*x + 225 | /
$$\int \frac{x}{\left(x^{4} + 12 x^{2}\right) + 225}\, dx = C + \frac{\sqrt{21} \operatorname{atan}{\left(\frac{\sqrt{21} \left(x^{2} + 6\right)}{63} \right)}}{126}$$
Gráfica
Respuesta
[src]
/ ____\ / ____\
____ |2*\/ 21 | ____ |8*\/ 21 |
\/ 21 *atan|--------| \/ 21 *atan|--------|
\ 21 / \ 63 /
- --------------------- + ---------------------
126 126
$$- \frac{\sqrt{21} \operatorname{atan}{\left(\frac{2 \sqrt{21}}{21} \right)}}{126} + \frac{\sqrt{21} \operatorname{atan}{\left(\frac{8 \sqrt{21}}{63} \right)}}{126}$$
=
=
/ ____\ / ____\
____ |2*\/ 21 | ____ |8*\/ 21 |
\/ 21 *atan|--------| \/ 21 *atan|--------|
\ 21 / \ 63 /
- --------------------- + ---------------------
126 126
$$- \frac{\sqrt{21} \operatorname{atan}{\left(\frac{2 \sqrt{21}}{21} \right)}}{126} + \frac{\sqrt{21} \operatorname{atan}{\left(\frac{8 \sqrt{21}}{63} \right)}}{126}$$
-sqrt(21)*atan(2*sqrt(21)/21)/126 + sqrt(21)*atan(8*sqrt(21)/63)/126
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.