Sr Examen
Integral de 9/((x-5)*(x^2+2x+10)) dx
Solución
Ha introducido
[src]
1 / | | 9 | ----------------------- dx | / 2 \ | (x - 5)*\x + 2*x + 10/ | / 0
$$\int\limits_{0}^{1} \frac{9}{\left(x - 5\right) \left(\left(x^{2} + 2 x\right) + 10\right)}\, dx$$
Integral(9/(((x - 5)*(x^2 + 2*x + 10))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /1 x\ | 2*atan|- + -| / 2 \ | 9 \3 3/ log\10 + x + 2*x/ log(-5 + x) | ----------------------- dx = C - ------------- - ------------------ + ----------- | / 2 \ 5 10 5 | (x - 5)*\x + 2*x + 10/ | /
$$\int \frac{9}{\left(x - 5\right) \left(\left(x^{2} + 2 x\right) + 10\right)}\, dx = C + \frac{\log{\left(x - 5 \right)}}{5} - \frac{\log{\left(x^{2} + 2 x + 10 \right)}}{10} - \frac{2 \operatorname{atan}{\left(\frac{x}{3} + \frac{1}{3} \right)}}{5}$$
Gráfica
Respuesta
[src]
2*atan(2/3) log(5) log(13) log(4) log(10) 2*atan(1/3)
- ----------- - ------ - ------- + ------ + ------- + -----------
5 5 10 5 10 5
$$- \frac{\log{\left(5 \right)}}{5} - \frac{\log{\left(13 \right)}}{10} - \frac{2 \operatorname{atan}{\left(\frac{2}{3} \right)}}{5} + \frac{2 \operatorname{atan}{\left(\frac{1}{3} \right)}}{5} + \frac{\log{\left(10 \right)}}{10} + \frac{\log{\left(4 \right)}}{5}$$
=
=
2*atan(2/3) log(5) log(13) log(4) log(10) 2*atan(1/3)
- ----------- - ------ - ------- + ------ + ------- + -----------
5 5 10 5 10 5
$$- \frac{\log{\left(5 \right)}}{5} - \frac{\log{\left(13 \right)}}{10} - \frac{2 \operatorname{atan}{\left(\frac{2}{3} \right)}}{5} + \frac{2 \operatorname{atan}{\left(\frac{1}{3} \right)}}{5} + \frac{\log{\left(10 \right)}}{10} + \frac{\log{\left(4 \right)}}{5}$$
-2*atan(2/3)/5 - log(5)/5 - log(13)/10 + log(4)/5 + log(10)/10 + 2*atan(1/3)/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.