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