Sr Examen
Integral de (3x^3+7x^2+9x+3)/((x+1)^2(x^2+2x+3)) dx
Solución
Ha introducido
[src]
1 / | | 3 2 | 3*x + 7*x + 9*x + 3 | ----------------------- dx | 2 / 2 \ | (x + 1) *\x + 2*x + 3/ | / 0
$$\int\limits_{0}^{1} \frac{\left(9 x + \left(3 x^{3} + 7 x^{2}\right)\right) + 3}{\left(x + 1\right)^{2} \left(\left(x^{2} + 2 x\right) + 3\right)}\, dx$$
Integral((3*x^3 + 7*x^2 + 9*x + 3)/(((x + 1)^2*(x^2 + 2*x + 3))), (x, 0, 1))
Gráfica
Respuesta
[src]
/ ___\
___ |\/ 2 |
\/ 2 *atan|-----| ___ / ___\
1 log(6) log(3) \ 2 / \/ 2 *atan\\/ 2 /
- - + ------ + 2*log(2) - ------ + ----------------- - -----------------
2 2 2 2 2
$$- \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \right)}}{2} - \frac{\log{\left(3 \right)}}{2} - \frac{1}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} + \frac{\log{\left(6 \right)}}{2} + 2 \log{\left(2 \right)}$$
=
=
/ ___\
___ |\/ 2 |
\/ 2 *atan|-----| ___ / ___\
1 log(6) log(3) \ 2 / \/ 2 *atan\\/ 2 /
- - + ------ + 2*log(2) - ------ + ----------------- - -----------------
2 2 2 2 2
$$- \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \right)}}{2} - \frac{\log{\left(3 \right)}}{2} - \frac{1}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} + \frac{\log{\left(6 \right)}}{2} + 2 \log{\left(2 \right)}$$
-1/2 + log(6)/2 + 2*log(2) - log(3)/2 + sqrt(2)*atan(sqrt(2)/2)/2 - sqrt(2)*atan(sqrt(2))/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.