Sr Examen
Integral de (3x+4)/((x^2-5x+9)(x+7)) dx
Solución
Ha introducido
[src]
1 / | | 3*x + 4 | ---------------------- dx | / 2 \ | \x - 5*x + 9/*(x + 7) | / 0
$$\int\limits_{0}^{1} \frac{3 x + 4}{\left(x + 7\right) \left(\left(x^{2} - 5 x\right) + 9\right)}\, dx$$
Integral((3*x + 4)/(((x^2 - 5*x + 9)*(x + 7))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ____ \ / ____ |2*\/ 11 *(-5/2 + x)| | / 2 \ 235*\/ 11 *atan|-------------------| | 3*x + 4 17*log(7 + x) 17*log\9 + x - 5*x/ \ 11 / | ---------------------- dx = C - ------------- + -------------------- + ------------------------------------ | / 2 \ 93 186 1023 | \x - 5*x + 9/*(x + 7) | /
$$\int \frac{3 x + 4}{\left(x + 7\right) \left(\left(x^{2} - 5 x\right) + 9\right)}\, dx = C - \frac{17 \log{\left(x + 7 \right)}}{93} + \frac{17 \log{\left(x^{2} - 5 x + 9 \right)}}{186} + \frac{235 \sqrt{11} \operatorname{atan}{\left(\frac{2 \sqrt{11} \left(x - \frac{5}{2}\right)}{11} \right)}}{1023}$$
Gráfica
Respuesta
[src]
/ ____\ / ____\
____ |3*\/ 11 | ____ |5*\/ 11 |
235*\/ 11 *atan|--------| 235*\/ 11 *atan|--------|
17*log(8) 17*log(9) 17*log(7) 17*log(5) \ 11 / \ 11 /
- --------- - --------- + --------- + --------- - ------------------------- + -------------------------
93 186 93 186 1023 1023
$$- \frac{235 \sqrt{11} \operatorname{atan}{\left(\frac{3 \sqrt{11}}{11} \right)}}{1023} - \frac{17 \log{\left(8 \right)}}{93} - \frac{17 \log{\left(9 \right)}}{186} + \frac{17 \log{\left(5 \right)}}{186} + \frac{17 \log{\left(7 \right)}}{93} + \frac{235 \sqrt{11} \operatorname{atan}{\left(\frac{5 \sqrt{11}}{11} \right)}}{1023}$$
=
=
/ ____\ / ____\
____ |3*\/ 11 | ____ |5*\/ 11 |
235*\/ 11 *atan|--------| 235*\/ 11 *atan|--------|
17*log(8) 17*log(9) 17*log(7) 17*log(5) \ 11 / \ 11 /
- --------- - --------- + --------- + --------- - ------------------------- + -------------------------
93 186 93 186 1023 1023
$$- \frac{235 \sqrt{11} \operatorname{atan}{\left(\frac{3 \sqrt{11}}{11} \right)}}{1023} - \frac{17 \log{\left(8 \right)}}{93} - \frac{17 \log{\left(9 \right)}}{186} + \frac{17 \log{\left(5 \right)}}{186} + \frac{17 \log{\left(7 \right)}}{93} + \frac{235 \sqrt{11} \operatorname{atan}{\left(\frac{5 \sqrt{11}}{11} \right)}}{1023}$$
-17*log(8)/93 - 17*log(9)/186 + 17*log(7)/93 + 17*log(5)/186 - 235*sqrt(11)*atan(3*sqrt(11)/11)/1023 + 235*sqrt(11)*atan(5*sqrt(11)/11)/1023
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.