Sr Examen
Integral de (x^3+8x^2+22x+7)/((x+1)(x^2+6x+13)) dx
Solución
Ha introducido
[src]
1 / | | 3 2 | x + 8*x + 22*x + 7 | ----------------------- dx | / 2 \ | (x + 1)*\x + 6*x + 13/ | / 0
$$\int\limits_{0}^{1} \frac{\left(22 x + \left(x^{3} + 8 x^{2}\right)\right) + 7}{\left(x + 1\right) \left(\left(x^{2} + 6 x\right) + 13\right)}\, dx$$
Integral((x^3 + 8*x^2 + 22*x + 7)/(((x + 1)*(x^2 + 6*x + 13))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | /3 x\ | 3 2 atan|- + -| | x + 8*x + 22*x + 7 \2 2/ / 2 \ | ----------------------- dx = C + x + ----------- - log(1 + x) + log\13 + x + 6*x/ | / 2 \ 2 | (x + 1)*\x + 6*x + 13/ | /
$$\int \frac{\left(22 x + \left(x^{3} + 8 x^{2}\right)\right) + 7}{\left(x + 1\right) \left(\left(x^{2} + 6 x\right) + 13\right)}\, dx = C + x - \log{\left(x + 1 \right)} + \log{\left(x^{2} + 6 x + 13 \right)} + \frac{\operatorname{atan}{\left(\frac{x}{2} + \frac{3}{2} \right)}}{2}$$
Gráfica
Respuesta
[src]
atan(2) atan(3/2)
1 + ------- - log(2) - log(13) - --------- + log(20)
2 2
$$- \log{\left(13 \right)} - \log{\left(2 \right)} - \frac{\operatorname{atan}{\left(\frac{3}{2} \right)}}{2} + \frac{\operatorname{atan}{\left(2 \right)}}{2} + 1 + \log{\left(20 \right)}$$
=
=
atan(2) atan(3/2)
1 + ------- - log(2) - log(13) - --------- + log(20)
2 2
$$- \log{\left(13 \right)} - \log{\left(2 \right)} - \frac{\operatorname{atan}{\left(\frac{3}{2} \right)}}{2} + \frac{\operatorname{atan}{\left(2 \right)}}{2} + 1 + \log{\left(20 \right)}$$
1 + atan(2)/2 - log(2) - log(13) - atan(3/2)/2 + log(20)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.