Judge the convergence and divergence of the following generalized integral ∫ x ^ 3E ^ (- x ^ 2) DX, [0, ∞]

Judge the convergence and divergence of the following generalized integral ∫ x ^ 3E ^ (- x ^ 2) DX, [0, ∞]

Direct calculation
=1/2∫(0,+∞) x^2e^(-x^2)dx^2
=1/2∫(0,+∞) te^(-t)dt
=1/2∫(0,+∞) e^(-t)dt
=1/2

Let the generalized integral ∫ (E → + infinity) f (x) DX converge and satisfy the equation f (x) = 2 / (divided by) x ^ 2-1 / (divided by) x times the square of LNX ∫ (E → + Nil)

Unexpectedly only me can help you?Don't mind I say English.Let N = ∫(e→+∞) f(x) dx,since this integral is convergent,it's a constantf(x) = 2/x² - 1/(xln²x) · ∫(e→+∞)f(x) = 2/x² -...

Finding definite integral ∫ superscript e subscript 1 (1 + LNX / x) DX
It's better to be more detailed,

∫ superscript e subscript 1 (1 + LNX / x) DX
=∫(1,e)(1+lnx)d(1+lnx)
=1/2 (1+lnx)²|(1,e)
=1/2 (2²-1)
=3/2

The root sign of cos2x-2a (2 + 2cosx) is equal to - 3 / 2
RT

3 radical cos