- #1
happyparticle
- 448
- 21
- Homework Statement
- Solve ##\int_{-\infty}^{\infty} (xa^3 e^{-x^2} + ab e^{-x^2}) dx##
- Relevant Equations
- ##\int_{-\infty}^{\infty} d e^{-u^2} dx = \sqrt{\pi}##
##\int_{-\infty}^{\infty} xe^{-x^2} = 0##
I'm trying to solve an improper integral, but I'm not familiar with this kind of integral.
##\int_{-\infty}^{\infty} (xa^3 e^{-x^2} + ab e^{-x^2}) dx##
a and b are both constants.
From what I found
##\int_{-\infty}^{\infty} d e^{-u^2} dx = \sqrt{\pi}##, where d is a constant
and
##\int_{-\infty}^{\infty} xe^{-x^2} = 0##
Is it correct to say that ##\int_{-\infty}^{\infty} (xa^3 e^{-x^2} + ab e^{-x^2}) dx = \sqrt{\pi}## ?
It seems like the constants doesn't affect the final result.
##\int_{-\infty}^{\infty} (xa^3 e^{-x^2} + ab e^{-x^2}) dx##
a and b are both constants.
From what I found
##\int_{-\infty}^{\infty} d e^{-u^2} dx = \sqrt{\pi}##, where d is a constant
and
##\int_{-\infty}^{\infty} xe^{-x^2} = 0##
Is it correct to say that ##\int_{-\infty}^{\infty} (xa^3 e^{-x^2} + ab e^{-x^2}) dx = \sqrt{\pi}## ?
It seems like the constants doesn't affect the final result.