Sr Examen
Integral de x*exp((-a)*|x|)*exp(i*x*K) dx
Solución
Ha introducido
[src]
pi / | | -a*|x| I*x*k | x*e *e dx | / -pi
$$\int\limits_{- \pi}^{\pi} x e^{- a \left|{x}\right|} e^{k i x}\, dx$$
Integral((x*exp((-a)*|x|))*exp((i*x)*k), (x, -pi, pi))
Respuesta (Indefinida)
[src]
/ / | | | -a*|x| I*x*k | -a*|x| I*x*k | x*e *e dx = C + | x*e *e dx | | / /
$$\int x e^{- a \left|{x}\right|} e^{k i x}\, dx = C + \int x e^{- a \left|{x}\right|} e^{k i x}\, dx$$
Respuesta
[src]
3 3 3 3 3 pi*I*k 2 2 3 -pi*a -pi*I*k 4 pi*I*k 4 pi*I*k 3 pi*I*k 2 2 2 pi*I*k 4 -pi*a -pi*I*k 4 -pi*a -pi*I*k 3 -pi*a -pi*I*k 2 -pi*a -pi*I*k 2 pi*I*k 2 2 pi*I*k 2 2 -pi*a -pi*I*k 3 pi*I*k 2 -pi*a -pi*I*k 3 pi*I*k 3 -pi*a -pi*I*k 3 -pi*a -pi*I*k
a a I*k I*k a *e 3*a*k 3*a*k a *e *e pi*a *e pi*k *e I*k *e 3*I*k*a 3*I*k*a 3*a*k *e pi*a *e *e pi*k *e *e I*k *e *e 3*a*k *e *e 3*I*k*a *e 6*pi*a *k *e 6*pi*a *k *e *e 4*pi*I*a*k *e 3*I*k*a *e *e 4*pi*I*k*a *e 4*pi*I*a*k *e *e 4*pi*I*k*a *e *e
----------------------------------------------------- - ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- - ----------------------------------------------------------------------------------------- - ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- - ----------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- + ----------------------------------------------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- + ----------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------------------------------------------- - ----------------------------------------------------- + -----------------------------------------------------
5 5 3 2 4 4 2 3 5 5 3 2 4 2 3 4 5 5 3 2 4 2 3 4 5 5 3 2 4 4 2 3 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 5 3 2 4 4 2 3 5 5 3 2 4 2 3 4 5 5 3 2 4 2 3 4 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 5 3 2 4 2 3 4 5 5 3 2 4 4 2 3 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 5 3 2 4 2 3 4 5 5 3 2 4 2 3 4 5 5 3 2 4 2 3 4 5 5 3 2 4 2 3 4 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 5 3 2 4 2 3 4 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 5 3 2 4 2 3 4 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 5 3 2 4 2 3 4 5 5 3 2 4 2 3 4
a - I*k - 10*a *k + 5*a*k - 5*I*k*a + 10*I*a *k a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a - I*k - 10*a *k + 5*a*k - 5*I*k*a + 10*I*a *k a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a - I*k - 10*a *k + 5*a*k - 5*I*k*a + 10*I*a *k a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a - I*k - 10*a *k + 5*a*k - 5*I*k*a + 10*I*a *k a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a
$$- \frac{\pi a^{4} e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} + \frac{\pi a^{4} e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} + \frac{4 i \pi a^{3} k e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} + \frac{4 i \pi a^{3} k e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} - \frac{a^{3} e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} - \frac{a^{3}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} + \frac{a^{3} e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} + \frac{a^{3}}{a^{5} - 5 i a^{4} k - 10 a^{3} k^{2} + 10 i a^{2} k^{3} + 5 a k^{4} - i k^{5}} + \frac{6 \pi a^{2} k^{2} e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} - \frac{6 \pi a^{2} k^{2} e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} + \frac{3 i a^{2} k e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} - \frac{3 i a^{2} k}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} + \frac{3 i a^{2} k e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} - \frac{3 i a^{2} k}{a^{5} - 5 i a^{4} k - 10 a^{3} k^{2} + 10 i a^{2} k^{3} + 5 a k^{4} - i k^{5}} - \frac{4 i \pi a k^{3} e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} - \frac{4 i \pi a k^{3} e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} + \frac{3 a k^{2} e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} + \frac{3 a k^{2}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} - \frac{3 a k^{2} e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} - \frac{3 a k^{2}}{a^{5} - 5 i a^{4} k - 10 a^{3} k^{2} + 10 i a^{2} k^{3} + 5 a k^{4} - i k^{5}} - \frac{\pi k^{4} e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} + \frac{\pi k^{4} e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} - \frac{i k^{3} e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} + \frac{i k^{3}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} - \frac{i k^{3} e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} + \frac{i k^{3}}{a^{5} - 5 i a^{4} k - 10 a^{3} k^{2} + 10 i a^{2} k^{3} + 5 a k^{4} - i k^{5}}$$
=
=
3 3 3 3 3 pi*I*k 2 2 3 -pi*a -pi*I*k 4 pi*I*k 4 pi*I*k 3 pi*I*k 2 2 2 pi*I*k 4 -pi*a -pi*I*k 4 -pi*a -pi*I*k 3 -pi*a -pi*I*k 2 -pi*a -pi*I*k 2 pi*I*k 2 2 pi*I*k 2 2 -pi*a -pi*I*k 3 pi*I*k 2 -pi*a -pi*I*k 3 pi*I*k 3 -pi*a -pi*I*k 3 -pi*a -pi*I*k
a a I*k I*k a *e 3*a*k 3*a*k a *e *e pi*a *e pi*k *e I*k *e 3*I*k*a 3*I*k*a 3*a*k *e pi*a *e *e pi*k *e *e I*k *e *e 3*a*k *e *e 3*I*k*a *e 6*pi*a *k *e 6*pi*a *k *e *e 4*pi*I*a*k *e 3*I*k*a *e *e 4*pi*I*k*a *e 4*pi*I*a*k *e *e 4*pi*I*k*a *e *e
----------------------------------------------------- - ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- - ----------------------------------------------------------------------------------------- - ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- - ----------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- + ----------------------------------------------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- + ----------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------------------------------------------- - ----------------------------------------------------- + -----------------------------------------------------
5 5 3 2 4 4 2 3 5 5 3 2 4 2 3 4 5 5 3 2 4 2 3 4 5 5 3 2 4 4 2 3 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 5 3 2 4 4 2 3 5 5 3 2 4 2 3 4 5 5 3 2 4 2 3 4 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 5 3 2 4 2 3 4 5 5 3 2 4 4 2 3 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 5 3 2 4 2 3 4 5 5 3 2 4 2 3 4 5 5 3 2 4 2 3 4 5 5 3 2 4 2 3 4 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 5 3 2 4 2 3 4 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 5 3 2 4 2 3 4 5 pi*a 5 pi*a 3 2 pi*a 4 pi*a 4 pi*a 2 3 pi*a 5 5 3 2 4 2 3 4 5 5 3 2 4 2 3 4
a - I*k - 10*a *k + 5*a*k - 5*I*k*a + 10*I*a *k a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a - I*k - 10*a *k + 5*a*k - 5*I*k*a + 10*I*a *k a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a - I*k - 10*a *k + 5*a*k - 5*I*k*a + 10*I*a *k a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a - I*k - 10*a *k + 5*a*k - 5*I*k*a + 10*I*a *k a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a *e - I*k *e - 10*a *k *e + 5*a*k *e - 5*I*k*a *e + 10*I*a *k *e a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a a + I*k - 10*a *k + 5*a*k - 10*I*a *k + 5*I*k*a
$$- \frac{\pi a^{4} e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} + \frac{\pi a^{4} e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} + \frac{4 i \pi a^{3} k e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} + \frac{4 i \pi a^{3} k e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} - \frac{a^{3} e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} - \frac{a^{3}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} + \frac{a^{3} e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} + \frac{a^{3}}{a^{5} - 5 i a^{4} k - 10 a^{3} k^{2} + 10 i a^{2} k^{3} + 5 a k^{4} - i k^{5}} + \frac{6 \pi a^{2} k^{2} e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} - \frac{6 \pi a^{2} k^{2} e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} + \frac{3 i a^{2} k e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} - \frac{3 i a^{2} k}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} + \frac{3 i a^{2} k e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} - \frac{3 i a^{2} k}{a^{5} - 5 i a^{4} k - 10 a^{3} k^{2} + 10 i a^{2} k^{3} + 5 a k^{4} - i k^{5}} - \frac{4 i \pi a k^{3} e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} - \frac{4 i \pi a k^{3} e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} + \frac{3 a k^{2} e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} + \frac{3 a k^{2}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} - \frac{3 a k^{2} e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} - \frac{3 a k^{2}}{a^{5} - 5 i a^{4} k - 10 a^{3} k^{2} + 10 i a^{2} k^{3} + 5 a k^{4} - i k^{5}} - \frac{\pi k^{4} e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} + \frac{\pi k^{4} e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} - \frac{i k^{3} e^{i \pi k}}{a^{5} e^{\pi a} - 5 i a^{4} k e^{\pi a} - 10 a^{3} k^{2} e^{\pi a} + 10 i a^{2} k^{3} e^{\pi a} + 5 a k^{4} e^{\pi a} - i k^{5} e^{\pi a}} + \frac{i k^{3}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} - \frac{i k^{3} e^{- \pi a} e^{- i \pi k}}{a^{5} + 5 i a^{4} k - 10 a^{3} k^{2} - 10 i a^{2} k^{3} + 5 a k^{4} + i k^{5}} + \frac{i k^{3}}{a^{5} - 5 i a^{4} k - 10 a^{3} k^{2} + 10 i a^{2} k^{3} + 5 a k^{4} - i k^{5}}$$
a^3/(a^5 - i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 5*i*k*a^4 + 10*i*a^2*k^3) - a^3/(a^5 + i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 10*i*a^2*k^3 + 5*i*k*a^4) + i*k^3/(a^5 + i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 10*i*a^2*k^3 + 5*i*k*a^4) + i*k^3/(a^5 - i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 5*i*k*a^4 + 10*i*a^2*k^3) - a^3*exp(pi*i*k)/(a^5*exp(pi*a) - i*k^5*exp(pi*a) - 10*a^3*k^2*exp(pi*a) + 5*a*k^4*exp(pi*a) - 5*i*k*a^4*exp(pi*a) + 10*i*a^2*k^3*exp(pi*a)) - 3*a*k^2/(a^5 - i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 5*i*k*a^4 + 10*i*a^2*k^3) + 3*a*k^2/(a^5 + i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 10*i*a^2*k^3 + 5*i*k*a^4) + a^3*exp(-pi*a)*exp(-pi*i*k)/(a^5 + i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 10*i*a^2*k^3 + 5*i*k*a^4) - pi*a^4*exp(pi*i*k)/(a^5*exp(pi*a) - i*k^5*exp(pi*a) - 10*a^3*k^2*exp(pi*a) + 5*a*k^4*exp(pi*a) - 5*i*k*a^4*exp(pi*a) + 10*i*a^2*k^3*exp(pi*a)) - pi*k^4*exp(pi*i*k)/(a^5*exp(pi*a) - i*k^5*exp(pi*a) - 10*a^3*k^2*exp(pi*a) + 5*a*k^4*exp(pi*a) - 5*i*k*a^4*exp(pi*a) + 10*i*a^2*k^3*exp(pi*a)) - i*k^3*exp(pi*i*k)/(a^5*exp(pi*a) - i*k^5*exp(pi*a) - 10*a^3*k^2*exp(pi*a) + 5*a*k^4*exp(pi*a) - 5*i*k*a^4*exp(pi*a) + 10*i*a^2*k^3*exp(pi*a)) - 3*i*k*a^2/(a^5 + i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 10*i*a^2*k^3 + 5*i*k*a^4) - 3*i*k*a^2/(a^5 - i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 5*i*k*a^4 + 10*i*a^2*k^3) + 3*a*k^2*exp(pi*i*k)/(a^5*exp(pi*a) - i*k^5*exp(pi*a) - 10*a^3*k^2*exp(pi*a) + 5*a*k^4*exp(pi*a) - 5*i*k*a^4*exp(pi*a) + 10*i*a^2*k^3*exp(pi*a)) + pi*a^4*exp(-pi*a)*exp(-pi*i*k)/(a^5 + i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 10*i*a^2*k^3 + 5*i*k*a^4) + pi*k^4*exp(-pi*a)*exp(-pi*i*k)/(a^5 + i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 10*i*a^2*k^3 + 5*i*k*a^4) - i*k^3*exp(-pi*a)*exp(-pi*i*k)/(a^5 + i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 10*i*a^2*k^3 + 5*i*k*a^4) - 3*a*k^2*exp(-pi*a)*exp(-pi*i*k)/(a^5 + i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 10*i*a^2*k^3 + 5*i*k*a^4) + 3*i*k*a^2*exp(pi*i*k)/(a^5*exp(pi*a) - i*k^5*exp(pi*a) - 10*a^3*k^2*exp(pi*a) + 5*a*k^4*exp(pi*a) - 5*i*k*a^4*exp(pi*a) + 10*i*a^2*k^3*exp(pi*a)) + 6*pi*a^2*k^2*exp(pi*i*k)/(a^5*exp(pi*a) - i*k^5*exp(pi*a) - 10*a^3*k^2*exp(pi*a) + 5*a*k^4*exp(pi*a) - 5*i*k*a^4*exp(pi*a) + 10*i*a^2*k^3*exp(pi*a)) - 6*pi*a^2*k^2*exp(-pi*a)*exp(-pi*i*k)/(a^5 + i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 10*i*a^2*k^3 + 5*i*k*a^4) - 4*pi*i*a*k^3*exp(pi*i*k)/(a^5*exp(pi*a) - i*k^5*exp(pi*a) - 10*a^3*k^2*exp(pi*a) + 5*a*k^4*exp(pi*a) - 5*i*k*a^4*exp(pi*a) + 10*i*a^2*k^3*exp(pi*a)) + 3*i*k*a^2*exp(-pi*a)*exp(-pi*i*k)/(a^5 + i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 10*i*a^2*k^3 + 5*i*k*a^4) + 4*pi*i*k*a^3*exp(pi*i*k)/(a^5*exp(pi*a) - i*k^5*exp(pi*a) - 10*a^3*k^2*exp(pi*a) + 5*a*k^4*exp(pi*a) - 5*i*k*a^4*exp(pi*a) + 10*i*a^2*k^3*exp(pi*a)) - 4*pi*i*a*k^3*exp(-pi*a)*exp(-pi*i*k)/(a^5 + i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 10*i*a^2*k^3 + 5*i*k*a^4) + 4*pi*i*k*a^3*exp(-pi*a)*exp(-pi*i*k)/(a^5 + i*k^5 - 10*a^3*k^2 + 5*a*k^4 - 10*i*a^2*k^3 + 5*i*k*a^4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.