Sr Examen
Integral de ((x^3)+(4*x^2)-5*x-7)/((x^2+9)(x-4)^2) dx
Solución
Ha introducido
[src]
1 / | | 3 2 | x + 4*x - 5*x - 7 | ------------------- dx | / 2 \ 2 | \x + 9/*(x - 4) | / 0
$$\int\limits_{0}^{1} \frac{\left(- 5 x + \left(x^{3} + 4 x^{2}\right)\right) - 7}{\left(x - 4\right)^{2} \left(x^{2} + 9\right)}\, dx$$
Integral((x^3 + 4*x^2 - 5*x - 7)/(((x^2 + 9)*(x - 4)^2)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | /x\ | 3 2 / 2\ 707*atan|-| | x + 4*x - 5*x - 7 221*log\9 + x / 101 \3/ 1067*log(-4 + x) | ------------------- dx = C - --------------- - ----------- + ----------- + ---------------- | / 2 \ 2 625 25*(-4 + x) 1875 625 | \x + 9/*(x - 4) | /
$$\int \frac{\left(- 5 x + \left(x^{3} + 4 x^{2}\right)\right) - 7}{\left(x - 4\right)^{2} \left(x^{2} + 9\right)}\, dx = C + \frac{1067 \log{\left(x - 4 \right)}}{625} - \frac{221 \log{\left(x^{2} + 9 \right)}}{625} + \frac{707 \operatorname{atan}{\left(\frac{x}{3} \right)}}{1875} - \frac{101}{25 \left(x - 4\right)}$$
Gráfica
Respuesta
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101 1067*log(4) 221*log(10) 221*log(9) 707*atan(1/3) 1067*log(3) --- - ----------- - ----------- + ---------- + ------------- + ----------- 300 625 625 625 1875 625
$$- \frac{1067 \log{\left(4 \right)}}{625} - \frac{221 \log{\left(10 \right)}}{625} + \frac{707 \operatorname{atan}{\left(\frac{1}{3} \right)}}{1875} + \frac{101}{300} + \frac{221 \log{\left(9 \right)}}{625} + \frac{1067 \log{\left(3 \right)}}{625}$$
=
=
101 1067*log(4) 221*log(10) 221*log(9) 707*atan(1/3) 1067*log(3) --- - ----------- - ----------- + ---------- + ------------- + ----------- 300 625 625 625 1875 625
$$- \frac{1067 \log{\left(4 \right)}}{625} - \frac{221 \log{\left(10 \right)}}{625} + \frac{707 \operatorname{atan}{\left(\frac{1}{3} \right)}}{1875} + \frac{101}{300} + \frac{221 \log{\left(9 \right)}}{625} + \frac{1067 \log{\left(3 \right)}}{625}$$
101/300 - 1067*log(4)/625 - 221*log(10)/625 + 221*log(9)/625 + 707*atan(1/3)/1875 + 1067*log(3)/625
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.