Nov 11, 2015 · The integral from $-\infty$ to $\infty$ is just twice this. So boom. If you want, you can rewrite $e^ {ix^2}=\cos (x^2)+i\sin (x^2)$ and equate the real and imaginary parts in the …

The integral which you describe has no closed form which is to say that it cannot be expressed in elementary functions. For example, you can express $\int x^2 \mathrm {d}x$ in elementary …

Integral of matrix exponential Ask Question Asked 11 years, 10 months ago Modified 1 year, 3 months ago

Jul 9, 2013 · So the integrand of the inner integral is holomorphic in $U$, for every $\omega$, by assumption. The triangle $\Delta$ is contained in $U$, so in your example, only triangles with …

Nov 23, 2025 · Closed 14 days ago. The integral $$\int_0^\infty \left (\dfrac {\sin x} {x}\right)^3dx$$ can be computed by contour integration.

If by integral you mean the cumulative distribution function $\Phi (x)$ mentioned in the comments by the OP, then your assertion is incorrect.

Oct 12, 2017 · This integral is one I can't solve. I have been trying to do it for the last two days, but can't get success. I can't do it by parts because the new integral thus formed will be even …

Feb 17, 2025 · The noun phrase "improper integral" written as $$ \int_a^\infty f (x) \, dx $$ is well defined. If the appropriate limit exists, we attach the property "convergent" to that expression …

Feb 9, 2011 · Try using the iterative definition of the Cantor function, which gives a sequence of functions that converge uniformly to the Cantor function; then integrate each of those (or try a …

Take the x2 x 2 and separate it as x⋅x x x. Then use integration by part taking x x as the function to differentiate, and xe−ax2 x e a x 2 as the function to integrate. Notice that xe−ax2 x e a x 2 …