Sr Examen
Integral de (x^3+x^2)/((2x^2-x+2)(x-2)) dx
Solución
Ha introducido
[src]
1 / | | 3 2 | x + x | ---------------------- dx | / 2 \ | \2*x - x + 2/*(x - 2) | / 0
$$\int\limits_{0}^{1} \frac{x^{3} + x^{2}}{\left(x - 2\right) \left(\left(2 x^{2} - x\right) + 2\right)}\, dx$$
Integral((x^3 + x^2)/(((2*x^2 - x + 2)*(x - 2))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ____ \ | ____ |4*\/ 15 *(-1/4 + x)| | 3 2 / 2\ \/ 15 *atan|-------------------| | x + x x log\2 - x + 2*x / 3*log(-2 + x) \ 15 / | ---------------------- dx = C + - + ----------------- + ------------- + -------------------------------- | / 2 \ 2 8 2 12 | \2*x - x + 2/*(x - 2) | /
$$\int \frac{x^{3} + x^{2}}{\left(x - 2\right) \left(\left(2 x^{2} - x\right) + 2\right)}\, dx = C + \frac{x}{2} + \frac{3 \log{\left(x - 2 \right)}}{2} + \frac{\log{\left(2 x^{2} - x + 2 \right)}}{8} + \frac{\sqrt{15} \operatorname{atan}{\left(\frac{4 \sqrt{15} \left(x - \frac{1}{4}\right)}{15} \right)}}{12}$$
Gráfica
Respuesta
[src]
/ ____\ / ____\
____ |\/ 15 | ____ |\/ 15 |
\/ 15 *atan|------| \/ 15 *atan|------|
1 3*log(2) log(3/2) \ 5 / \ 15 /
- - -------- + -------- + ------------------- + -------------------
2 2 8 12 12
$$- \frac{3 \log{\left(2 \right)}}{2} + \frac{\log{\left(\frac{3}{2} \right)}}{8} + \frac{\sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15}}{15} \right)}}{12} + \frac{\sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15}}{5} \right)}}{12} + \frac{1}{2}$$
=
=
/ ____\ / ____\
____ |\/ 15 | ____ |\/ 15 |
\/ 15 *atan|------| \/ 15 *atan|------|
1 3*log(2) log(3/2) \ 5 / \ 15 /
- - -------- + -------- + ------------------- + -------------------
2 2 8 12 12
$$- \frac{3 \log{\left(2 \right)}}{2} + \frac{\log{\left(\frac{3}{2} \right)}}{8} + \frac{\sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15}}{15} \right)}}{12} + \frac{\sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15}}{5} \right)}}{12} + \frac{1}{2}$$
1/2 - 3*log(2)/2 + log(3/2)/8 + sqrt(15)*atan(sqrt(15)/5)/12 + sqrt(15)*atan(sqrt(15)/15)/12
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.