Sr Examen
Integral de (x^2+8*x+1)/(x^3-8) dx
Solución
Ha introducido
[src]
1 / | | 2 | x + 8*x + 1 | ------------ dx | 3 | x - 8 | / 0
$$\int\limits_{0}^{1} \frac{\left(x^{2} + 8 x\right) + 1}{x^{3} - 8}\, dx$$
Integral((x^2 + 8*x + 1)/(x^3 - 8), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ___ \ | ___ |\/ 3 *(1 + x)| | 2 / 2 \ 5*\/ 3 *atan|-------------| | x + 8*x + 1 3*log\4 + x + 2*x/ 7*log(-2 + x) \ 3 / | ------------ dx = C - ------------------- + ------------- + --------------------------- | 3 8 4 4 | x - 8 | /
$$\int \frac{\left(x^{2} + 8 x\right) + 1}{x^{3} - 8}\, dx = C + \frac{7 \log{\left(x - 2 \right)}}{4} - \frac{3 \log{\left(x^{2} + 2 x + 4 \right)}}{8} + \frac{5 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x + 1\right)}{3} \right)}}{4}$$
Gráfica
Respuesta
[src]
/ ___\
___ |2*\/ 3 |
___ 5*\/ 3 *atan|-------|
7*log(2) 3*log(7) 3*log(4) 5*pi*\/ 3 \ 3 /
- -------- - -------- + -------- - ---------- + ---------------------
4 8 8 24 4
$$- \frac{7 \log{\left(2 \right)}}{4} - \frac{5 \sqrt{3} \pi}{24} - \frac{3 \log{\left(7 \right)}}{8} + \frac{3 \log{\left(4 \right)}}{8} + \frac{5 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{4}$$
=
=
/ ___\
___ |2*\/ 3 |
___ 5*\/ 3 *atan|-------|
7*log(2) 3*log(7) 3*log(4) 5*pi*\/ 3 \ 3 /
- -------- - -------- + -------- - ---------- + ---------------------
4 8 8 24 4
$$- \frac{7 \log{\left(2 \right)}}{4} - \frac{5 \sqrt{3} \pi}{24} - \frac{3 \log{\left(7 \right)}}{8} + \frac{3 \log{\left(4 \right)}}{8} + \frac{5 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{4}$$
-7*log(2)/4 - 3*log(7)/8 + 3*log(4)/8 - 5*pi*sqrt(3)/24 + 5*sqrt(3)*atan(2*sqrt(3)/3)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.