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