hoenir
Dec29-11, 05:38 PM
Is there any way to solve either of the following integrals
\int_{-\infty}^{\infty}{F(a + bx)f(x) dx} or \int_{-\infty}^{\infty}{F^{2}(a + bx)f(x) dx},
where F^\prime(x) = f(x) and \int_{-\infty}^{\infty}{f(x) dx} = 1.
I know that it is easy to integrate \int_{-\infty}^{\infty}{F(x)f(x) dx} using substitution, but are there any similar tricks to solve the above integrals?
\int_{-\infty}^{\infty}{F(a + bx)f(x) dx} or \int_{-\infty}^{\infty}{F^{2}(a + bx)f(x) dx},
where F^\prime(x) = f(x) and \int_{-\infty}^{\infty}{f(x) dx} = 1.
I know that it is easy to integrate \int_{-\infty}^{\infty}{F(x)f(x) dx} using substitution, but are there any similar tricks to solve the above integrals?