Sr Examen
Integral de (x^3+2*x+1)/(x^3-27) dx
Solución
Ha introducido
[src]
1 / | | 3 | x + 2*x + 1 | ------------ dx | 3 | x - 27 | / 0
$$\int\limits_{0}^{1} \frac{\left(x^{3} + 2 x\right) + 1}{x^{3} - 27}\, dx$$
Integral((x^3 + 2*x + 1)/(x^3 - 27), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ___ \ | ___ |2*\/ 3 *(3/2 + x)| | 3 / 2 \ 22*\/ 3 *atan|-----------------| | x + 2*x + 1 17*log\9 + x + 3*x/ 34*log(-3 + x) \ 9 / | ------------ dx = C + x - -------------------- + -------------- - -------------------------------- | 3 27 27 27 | x - 27 | /
$$\int \frac{\left(x^{3} + 2 x\right) + 1}{x^{3} - 27}\, dx = C + x + \frac{34 \log{\left(x - 3 \right)}}{27} - \frac{17 \log{\left(x^{2} + 3 x + 9 \right)}}{27} - \frac{22 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x + \frac{3}{2}\right)}{9} \right)}}{27}$$
Gráfica
Respuesta
[src]
/ ___\
___ |5*\/ 3 |
22*\/ 3 *atan|-------| ___
34*log(3) 17*log(13) 17*log(9) 34*log(2) \ 9 / 11*pi*\/ 3
1 - --------- - ---------- + --------- + --------- - ---------------------- + -----------
27 27 27 27 27 81
$$- \frac{17 \log{\left(13 \right)}}{27} - \frac{34 \log{\left(3 \right)}}{27} - \frac{22 \sqrt{3} \operatorname{atan}{\left(\frac{5 \sqrt{3}}{9} \right)}}{27} + \frac{11 \sqrt{3} \pi}{81} + \frac{34 \log{\left(2 \right)}}{27} + 1 + \frac{17 \log{\left(9 \right)}}{27}$$
=
=
/ ___\
___ |5*\/ 3 |
22*\/ 3 *atan|-------| ___
34*log(3) 17*log(13) 17*log(9) 34*log(2) \ 9 / 11*pi*\/ 3
1 - --------- - ---------- + --------- + --------- - ---------------------- + -----------
27 27 27 27 27 81
$$- \frac{17 \log{\left(13 \right)}}{27} - \frac{34 \log{\left(3 \right)}}{27} - \frac{22 \sqrt{3} \operatorname{atan}{\left(\frac{5 \sqrt{3}}{9} \right)}}{27} + \frac{11 \sqrt{3} \pi}{81} + \frac{34 \log{\left(2 \right)}}{27} + 1 + \frac{17 \log{\left(9 \right)}}{27}$$
1 - 34*log(3)/27 - 17*log(13)/27 + 17*log(9)/27 + 34*log(2)/27 - 22*sqrt(3)*atan(5*sqrt(3)/9)/27 + 11*pi*sqrt(3)/81
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.