Integrating Exponential Functions - Solving by Parts

forty
Messages
132
Reaction score
0
(x^2).e^(-2a(x^2))

how would i integrate this? By parts?

If so using |udv = uv - |vdu (hope that's right)

would i let u = x^2 and dv = e^(-2a(x^2)) ?

but how do I integrate dv = e^(-2a(x^2)) to find v ?

any help appreciated :)
 
Physics news on Phys.org
I think that integration by parts is the way to go, but there's more than one way to divide things up in this problem.

Try it this way:
u = x, dv = xe-2ax2dx

Now you have a dv that you have a hope of integrating (using an ordinary substitution).
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

Similar threads

Back
Top