Sr Examen
Integral de (4x-9)/((x-3)(x^2+x+4)) dx
Solución
Ha introducido
[src]
1 / | | 4*x - 9 | -------------------- dx | / 2 \ | (x - 3)*\x + x + 4/ | / 0
$$\int\limits_{0}^{1} \frac{4 x - 9}{\left(x - 3\right) \left(\left(x^{2} + x\right) + 4\right)}\, dx$$
Integral((4*x - 9)/(((x - 3)*(x^2 + x + 4))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ____ \ / ____ |2*\/ 15 *(1/2 + x)| | / 2\ 107*\/ 15 *atan|------------------| | 4*x - 9 3*log\4 + x + x / 3*log(-3 + x) \ 15 / | -------------------- dx = C - ----------------- + ------------- + ----------------------------------- | / 2 \ 32 16 240 | (x - 3)*\x + x + 4/ | /
$$\int \frac{4 x - 9}{\left(x - 3\right) \left(\left(x^{2} + x\right) + 4\right)}\, dx = C + \frac{3 \log{\left(x - 3 \right)}}{16} - \frac{3 \log{\left(x^{2} + x + 4 \right)}}{32} + \frac{107 \sqrt{15} \operatorname{atan}{\left(\frac{2 \sqrt{15} \left(x + \frac{1}{2}\right)}{15} \right)}}{240}$$
Gráfica
Respuesta
[src]
/ ____\ / ____\
____ |\/ 15 | ____ |\/ 15 |
107*\/ 15 *atan|------| 107*\/ 15 *atan|------|
3*log(3) 3*log(6) 3*log(2) 3*log(4) \ 15 / \ 5 /
- -------- - -------- + -------- + -------- - ----------------------- + -----------------------
16 32 16 32 240 240
$$- \frac{107 \sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15}}{15} \right)}}{240} - \frac{3 \log{\left(3 \right)}}{16} - \frac{3 \log{\left(6 \right)}}{32} + \frac{3 \log{\left(2 \right)}}{16} + \frac{3 \log{\left(4 \right)}}{32} + \frac{107 \sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15}}{5} \right)}}{240}$$
=
=
/ ____\ / ____\
____ |\/ 15 | ____ |\/ 15 |
107*\/ 15 *atan|------| 107*\/ 15 *atan|------|
3*log(3) 3*log(6) 3*log(2) 3*log(4) \ 15 / \ 5 /
- -------- - -------- + -------- + -------- - ----------------------- + -----------------------
16 32 16 32 240 240
$$- \frac{107 \sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15}}{15} \right)}}{240} - \frac{3 \log{\left(3 \right)}}{16} - \frac{3 \log{\left(6 \right)}}{32} + \frac{3 \log{\left(2 \right)}}{16} + \frac{3 \log{\left(4 \right)}}{32} + \frac{107 \sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15}}{5} \right)}}{240}$$
-3*log(3)/16 - 3*log(6)/32 + 3*log(2)/16 + 3*log(4)/32 - 107*sqrt(15)*atan(sqrt(15)/15)/240 + 107*sqrt(15)*atan(sqrt(15)/5)/240
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.