Sr Examen
Integral de 20dx/((x+4)*((x^2)+4x+20)) dx
Solución
Ha introducido
[src]
1 / | | 20 | ----------------------- dx | / 2 \ | (x + 4)*\x + 4*x + 20/ | / 0
$$\int\limits_{0}^{1} \frac{20}{\left(x + 4\right) \left(\left(x^{2} + 4 x\right) + 20\right)}\, dx$$
Integral(20/(((x + 4)*(x^2 + 4*x + 20))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /1 x\ | atan|- + -| / 2 \ | 20 \2 4/ log\20 + x + 4*x/ | ----------------------- dx = C + ----------- - ------------------ + log(4 + x) | / 2 \ 2 2 | (x + 4)*\x + 4*x + 20/ | /
$$\int \frac{20}{\left(x + 4\right) \left(\left(x^{2} + 4 x\right) + 20\right)}\, dx = C + \log{\left(x + 4 \right)} - \frac{\log{\left(x^{2} + 4 x + 20 \right)}}{2} + \frac{\operatorname{atan}{\left(\frac{x}{4} + \frac{1}{2} \right)}}{2}$$
Gráfica
Respuesta
[src]
atan(3/4) log(20) atan(1/2) log(25)
--------- + ------- - log(4) - --------- - ------- + log(5)
2 2 2 2
$$- \frac{\log{\left(25 \right)}}{2} - \log{\left(4 \right)} - \frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{2} + \frac{\operatorname{atan}{\left(\frac{3}{4} \right)}}{2} + \frac{\log{\left(20 \right)}}{2} + \log{\left(5 \right)}$$
=
=
atan(3/4) log(20) atan(1/2) log(25)
--------- + ------- - log(4) - --------- - ------- + log(5)
2 2 2 2
$$- \frac{\log{\left(25 \right)}}{2} - \log{\left(4 \right)} - \frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{2} + \frac{\operatorname{atan}{\left(\frac{3}{4} \right)}}{2} + \frac{\log{\left(20 \right)}}{2} + \log{\left(5 \right)}$$
atan(3/4)/2 + log(20)/2 - log(4) - atan(1/2)/2 - log(25)/2 + log(5)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.