Sr Examen
Integral de (x^4+2x^2+3)/(x^3-8) dx
Solución
Ha introducido
[src]
1 / | | 4 2 | x + 2*x + 3 | ------------- dx | 3 | x - 8 | / 0
$$\int\limits_{0}^{1} \frac{\left(x^{4} + 2 x^{2}\right) + 3}{x^{3} - 8}\, dx$$
Integral((x^4 + 2*x^2 + 3)/(x^3 - 8), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ___ \ | ___ |\/ 3 *(1 + x)| | 4 2 2 / 2 \ 13*\/ 3 *atan|-------------| | x + 2*x + 3 x log\4 + x + 2*x/ 9*log(-2 + x) \ 3 / | ------------- dx = C + -- - ----------------- + ------------- + ---------------------------- | 3 2 8 4 12 | x - 8 | /
$$\int \frac{\left(x^{4} + 2 x^{2}\right) + 3}{x^{3} - 8}\, dx = C + \frac{x^{2}}{2} + \frac{9 \log{\left(x - 2 \right)}}{4} - \frac{\log{\left(x^{2} + 2 x + 4 \right)}}{8} + \frac{13 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x + 1\right)}{3} \right)}}{12}$$
Gráfica
Respuesta
[src]
/ ___\
___ |2*\/ 3 |
___ 13*\/ 3 *atan|-------|
1 9*log(2) log(7) log(4) 13*pi*\/ 3 \ 3 /
- - -------- - ------ + ------ - ----------- + ----------------------
2 4 8 8 72 12
$$- \frac{9 \log{\left(2 \right)}}{4} - \frac{13 \sqrt{3} \pi}{72} - \frac{\log{\left(7 \right)}}{8} + \frac{\log{\left(4 \right)}}{8} + \frac{1}{2} + \frac{13 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{12}$$
=
=
/ ___\
___ |2*\/ 3 |
___ 13*\/ 3 *atan|-------|
1 9*log(2) log(7) log(4) 13*pi*\/ 3 \ 3 /
- - -------- - ------ + ------ - ----------- + ----------------------
2 4 8 8 72 12
$$- \frac{9 \log{\left(2 \right)}}{4} - \frac{13 \sqrt{3} \pi}{72} - \frac{\log{\left(7 \right)}}{8} + \frac{\log{\left(4 \right)}}{8} + \frac{1}{2} + \frac{13 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{12}$$
1/2 - 9*log(2)/4 - log(7)/8 + log(4)/8 - 13*pi*sqrt(3)/72 + 13*sqrt(3)*atan(2*sqrt(3)/3)/12
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.