help with integration of exponential... (1 Viewer)

[kangarulz]

integrate with respect to x:

xe^(x^2) + xe^(-x^2)

 

[Riviet]

I'll start you off:

Let u=x²
du/dx = 2x

x.e^x2 + x.e^-x2 = 1/2.(2x.e^x2) + 1/2.(2x.e^x2)

Hope that helps.

 

[hyparzero]

I'll start you off:

Let u=x²
du/dx = 2x

x.e^x2 + x.e^-x2 = 1/2.(2x.e^x2) + 1/2.(2x.e^x2)

Hope that helps.

no it doesnt

 

[alcalder]

integrate with respect to x:

xe^(x^2) + xe^(-x^2)

OK, the starting point is knowing that:

∫f'(x)e^f(x).dx = e^f(x) + c

SO

If we have

f(x) = e^x2
f'(x) = 2xe^x2

f(x) = e^-x2
f'(x) = -2xe^-x2

Now, you can do:

∫ (xe^x2) + xe^-x2)).dx =
∫ (xe^x2).dx +∫(xe^-x2).dx

= 1/2∫ (2xe^x2).dx -1/2∫(2xe^-x2).dx
= 1/2 (e^x2) - 1/2 (e^-x2) + c

Does that help??