Sr Examen
Integral de (-2x^2+x+10)/(x^3-5x+12) dx
Solución
Ha introducido
[src]
1 / | | 2 | - 2*x + x + 10 | --------------- dx | 3 | x - 5*x + 12 | / 0
$$\int\limits_{0}^{1} \frac{\left(- 2 x^{2} + x\right) + 10}{\left(x^{3} - 5 x\right) + 12}\, dx$$
Integral((-2*x^2 + x + 10)/(x^3 - 5*x + 12), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ___ \ | ___ |2*\/ 7 *(-3/2 + x)| | 2 / 2 \ \/ 7 *atan|------------------| | - 2*x + x + 10 3*log\4 + x - 3*x/ log(3 + x) \ 7 / | --------------- dx = C - ------------------- - ---------- + ------------------------------ | 3 4 2 2 | x - 5*x + 12 | /
$$\int \frac{\left(- 2 x^{2} + x\right) + 10}{\left(x^{3} - 5 x\right) + 12}\, dx = C - \frac{\log{\left(x + 3 \right)}}{2} - \frac{3 \log{\left(x^{2} - 3 x + 4 \right)}}{4} + \frac{\sqrt{7} \operatorname{atan}{\left(\frac{2 \sqrt{7} \left(x - \frac{3}{2}\right)}{7} \right)}}{2}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\
___ |3*\/ 7 | ___ |\/ 7 |
\/ 7 *atan|-------| \/ 7 *atan|-----|
log(3) 3*log(2) log(4) \ 7 / \ 7 /
------ - -------- + ------ + ------------------- - -----------------
2 4 4 2 2
$$- \frac{3 \log{\left(2 \right)}}{4} - \frac{\sqrt{7} \operatorname{atan}{\left(\frac{\sqrt{7}}{7} \right)}}{2} + \frac{\log{\left(4 \right)}}{4} + \frac{\log{\left(3 \right)}}{2} + \frac{\sqrt{7} \operatorname{atan}{\left(\frac{3 \sqrt{7}}{7} \right)}}{2}$$
=
=
/ ___\ / ___\
___ |3*\/ 7 | ___ |\/ 7 |
\/ 7 *atan|-------| \/ 7 *atan|-----|
log(3) 3*log(2) log(4) \ 7 / \ 7 /
------ - -------- + ------ + ------------------- - -----------------
2 4 4 2 2
$$- \frac{3 \log{\left(2 \right)}}{4} - \frac{\sqrt{7} \operatorname{atan}{\left(\frac{\sqrt{7}}{7} \right)}}{2} + \frac{\log{\left(4 \right)}}{4} + \frac{\log{\left(3 \right)}}{2} + \frac{\sqrt{7} \operatorname{atan}{\left(\frac{3 \sqrt{7}}{7} \right)}}{2}$$
log(3)/2 - 3*log(2)/4 + log(4)/4 + sqrt(7)*atan(3*sqrt(7)/7)/2 - sqrt(7)*atan(sqrt(7)/7)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.