List questions from improper-integrals

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List Question

Estimate $\int_0^{\infty} 1/\sqrt{1+x^4} \mathrm{d}x$

Evaluate the integration?

The unbeatable $\int e^{1/\cos(x)} dx$ integral

Finding $\int_{-\infty}^{\infty}e^{x^2}\,dx$

How do I integrate $x^{\frac{3}{2}}e^{-x}$ from 0 to inf?

Convergence of the improper integral $\int_{0}^{\pi/2}\tan^{p}(x) \; dx$

How to integrate $e^{-\frac{x^2}{4}}\cos(x)$

Improper Riemann integral and imaginary exponential of real polynomials

Integration of complex function: $\int_{-\infty}^{\infty}e ^{-\pi(x^2a^2+2iux)}\,dx$

convergence of $\int _1^{\infty} \sin\big(\mathrm{e}^x(x-2)\big)\,dx$

A question in integral convergence

Improper parametric integral and differentiation under the integral sign

Solving Integral that contain exponential and Power

Numerical integration of innocent-looking singular integrand

Compute $\int_0^\infty\frac{\cos(xt)}{1+t^2}dt$

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