- #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.