Sr Examen
Integral de (2x+1)÷((x-2)(x^2+x+2)) dx
Solución
Ha introducido
[src]
1 / | | 2*x + 1 | -------------------- dx | / 2 \ | (x - 2)*\x + x + 2/ | / 0
$$\int\limits_{0}^{1} \frac{2 x + 1}{\left(x - 2\right) \left(\left(x^{2} + x\right) + 2\right)}\, dx$$
Integral((2*x + 1)/(((x - 2)*(x^2 + x + 2))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ \ / ___ |2*\/ 7 *(1/2 + x)| | / 2\ \/ 7 *atan|-----------------| | 2*x + 1 5*log\2 + x + x / 5*log(-2 + x) \ 7 / | -------------------- dx = C - ----------------- + ------------- + ----------------------------- | / 2 \ 16 8 8 | (x - 2)*\x + x + 2/ | /
$$\int \frac{2 x + 1}{\left(x - 2\right) \left(\left(x^{2} + x\right) + 2\right)}\, dx = C + \frac{5 \log{\left(x - 2 \right)}}{8} - \frac{5 \log{\left(x^{2} + x + 2 \right)}}{16} + \frac{\sqrt{7} \operatorname{atan}{\left(\frac{2 \sqrt{7} \left(x + \frac{1}{2}\right)}{7} \right)}}{8}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\
___ |\/ 7 | ___ |3*\/ 7 |
\/ 7 *atan|-----| \/ 7 *atan|-------|
5*log(2) 5*log(4) \ 7 / \ 7 /
- -------- - -------- - ----------------- + -------------------
16 16 8 8
$$- \frac{5 \log{\left(4 \right)}}{16} - \frac{5 \log{\left(2 \right)}}{16} - \frac{\sqrt{7} \operatorname{atan}{\left(\frac{\sqrt{7}}{7} \right)}}{8} + \frac{\sqrt{7} \operatorname{atan}{\left(\frac{3 \sqrt{7}}{7} \right)}}{8}$$
=
=
/ ___\ / ___\
___ |\/ 7 | ___ |3*\/ 7 |
\/ 7 *atan|-----| \/ 7 *atan|-------|
5*log(2) 5*log(4) \ 7 / \ 7 /
- -------- - -------- - ----------------- + -------------------
16 16 8 8
$$- \frac{5 \log{\left(4 \right)}}{16} - \frac{5 \log{\left(2 \right)}}{16} - \frac{\sqrt{7} \operatorname{atan}{\left(\frac{\sqrt{7}}{7} \right)}}{8} + \frac{\sqrt{7} \operatorname{atan}{\left(\frac{3 \sqrt{7}}{7} \right)}}{8}$$
-5*log(2)/16 - 5*log(4)/16 - sqrt(7)*atan(sqrt(7)/7)/8 + sqrt(7)*atan(3*sqrt(7)/7)/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.