Sr Examen
Integral de x^2/(2x^2+3)^2 dx
Solución
Ha introducido
[src]
1 / | | 2 | x | ----------- dx | 2 | / 2 \ | \2*x + 3/ | / 0
$$\int\limits_{0}^{1} \frac{x^{2}}{\left(2 x^{2} + 3\right)^{2}}\, dx$$
Integral(x^2/(2*x^2 + 3)^2, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ___\ \
| |x*\/ 6 | |
|atan|-------| ___ |
/ ___ | \ 3 / x*\/ 6 | / ___\
| \/ 6 *|------------- + ------------| ___ |x*\/ 6 |
| 2 | 2 / 2\| \/ 6 *atan|-------|
| x \ 2*\3 + 2*x // \ 3 /
| ----------- dx = C - ------------------------------------ + -------------------
| 2 12 12
| / 2 \
| \2*x + 3/
|
/
$$\int \frac{x^{2}}{\left(2 x^{2} + 3\right)^{2}}\, dx = C - \frac{\sqrt{6} \left(\frac{\sqrt{6} x}{2 \left(2 x^{2} + 3\right)} + \frac{\operatorname{atan}{\left(\frac{\sqrt{6} x}{3} \right)}}{2}\right)}{12} + \frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} \right)}}{12}$$
Gráfica
Respuesta
[src]
/ ___\
___ |\/ 6 |
\/ 6 *atan|-----|
1 \ 3 /
- -- + -----------------
20 24
$$- \frac{1}{20} + \frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6}}{3} \right)}}{24}$$
=
=
/ ___\
___ |\/ 6 |
\/ 6 *atan|-----|
1 \ 3 /
- -- + -----------------
20 24
$$- \frac{1}{20} + \frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6}}{3} \right)}}{24}$$
-1/20 + sqrt(6)*atan(sqrt(6)/3)/24
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.