Sr Examen
Integral de 1/(m^2+x^2)^2 dx
Solución
Ha introducido
[src]
400 / | | 1 | ---------- dx | 2 | / 2 2\ | \m + x / | / 0
$$\int\limits_{0}^{400} \frac{1}{\left(m^{2} + x^{2}\right)^{2}}\, dx$$
Integral(1/((m^2 + x^2)^2), (x, 0, 400))
Respuesta (Indefinida)
[src]
/ I*log(x - I*m) I*log(x + I*m) | - -------------- + -------------- | 1 x 4 4 | ---------- dx = C + -------------- + --------------------------------- | 2 4 2 2 3 | / 2 2\ 2*m + 2*m *x m | \m + x / | /
$$\int \frac{1}{\left(m^{2} + x^{2}\right)^{2}}\, dx = C + \frac{x}{2 m^{4} + 2 m^{2} x^{2}} + \frac{- \frac{i \log{\left(- i m + x \right)}}{4} + \frac{i \log{\left(i m + x \right)}}{4}}{m^{3}}$$
Respuesta
[src]
I*log(400 - I*m) I*log(400 + I*m) I*log(-I*m) I*log(I*m)
- ---------------- + ---------------- - ----------- + ----------
400 4 4 4 4
---------------- + ------------------------------------- - --------------------------
4 2 3 3
2*m + 320000*m m m
$$\frac{400}{2 m^{4} + 320000 m^{2}} - \frac{- \frac{i \log{\left(- i m \right)}}{4} + \frac{i \log{\left(i m \right)}}{4}}{m^{3}} + \frac{- \frac{i \log{\left(- i m + 400 \right)}}{4} + \frac{i \log{\left(i m + 400 \right)}}{4}}{m^{3}}$$
=
=
I*log(400 - I*m) I*log(400 + I*m) I*log(-I*m) I*log(I*m)
- ---------------- + ---------------- - ----------- + ----------
400 4 4 4 4
---------------- + ------------------------------------- - --------------------------
4 2 3 3
2*m + 320000*m m m
$$\frac{400}{2 m^{4} + 320000 m^{2}} - \frac{- \frac{i \log{\left(- i m \right)}}{4} + \frac{i \log{\left(i m \right)}}{4}}{m^{3}} + \frac{- \frac{i \log{\left(- i m + 400 \right)}}{4} + \frac{i \log{\left(i m + 400 \right)}}{4}}{m^{3}}$$
400/(2*m^4 + 320000*m^2) + (-i*log(400 - i*m)/4 + i*log(400 + i*m)/4)/m^3 - (-i*log(-i*m)/4 + i*log(i*m)/4)/m^3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.