Sr Examen
Integral de (6x-2)/((x^2+2)(x+3)) dx
Solución
Ha introducido
[src]
1 / | | 6*x - 2 | ---------------- dx | / 2 \ | \x + 2/*(x + 3) | / 0
$$\int\limits_{0}^{1} \frac{6 x - 2}{\left(x + 3\right) \left(x^{2} + 2\right)}\, dx$$
Integral((6*x - 2)/(((x^2 + 2)*(x + 3))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___\ / ___ |x*\/ 2 | | / 2\ 3*\/ 2 *atan|-------| | 6*x - 2 20*log(3 + x) 10*log\2 + x / \ 2 / | ---------------- dx = C - ------------- + -------------- + --------------------- | / 2 \ 11 11 11 | \x + 2/*(x + 3) | /
$$\int \frac{6 x - 2}{\left(x + 3\right) \left(x^{2} + 2\right)}\, dx = C - \frac{20 \log{\left(x + 3 \right)}}{11} + \frac{10 \log{\left(x^{2} + 2 \right)}}{11} + \frac{3 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{11}$$
Gráfica
Respuesta
[src]
/ ___\
___ |\/ 2 |
3*\/ 2 *atan|-----|
20*log(4) 10*log(2) 30*log(3) \ 2 /
- --------- - --------- + --------- + -------------------
11 11 11 11
$$- \frac{20 \log{\left(4 \right)}}{11} - \frac{10 \log{\left(2 \right)}}{11} + \frac{3 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{11} + \frac{30 \log{\left(3 \right)}}{11}$$
=
=
/ ___\
___ |\/ 2 |
3*\/ 2 *atan|-----|
20*log(4) 10*log(2) 30*log(3) \ 2 /
- --------- - --------- + --------- + -------------------
11 11 11 11
$$- \frac{20 \log{\left(4 \right)}}{11} - \frac{10 \log{\left(2 \right)}}{11} + \frac{3 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{11} + \frac{30 \log{\left(3 \right)}}{11}$$
-20*log(4)/11 - 10*log(2)/11 + 30*log(3)/11 + 3*sqrt(2)*atan(sqrt(2)/2)/11
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.