Feb 21, 2018 · I was trying to do this integral $$\int \sqrt {1+x^2}dx$$ I saw this question and its' use of hyperbolic functions. I did it with binomial differential method since the given integral is …

May 15, 2023 · Similar to the link: Why I can't reduce an integral divided by another integral? I caught a similar situation that looks like this question. I read the book named Advanced …

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 …

May 28, 2021 · We derive by comparison with the real case (evaluation of a real Gaussian integral, which clearly has a positive value), that the solution with a positive real part is the …

I was reading on Wikipedia in this article about the n-dimensional and functional generalization of the Gaussian integral. In particular, I would like to understand how the following equations are

Answers to the question of the integral of $\frac {1} {x}$ are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers.

Mar 31, 2016 · Definite integral of sign function Ask Question Asked 9 years, 7 months ago Modified 3 years, 1 month ago

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

I don't get the question either. Assuming that the integral is welldefined, it evaluates to a number, which you then take to a power. What kind of formula do you expect?

For an integral of the form $$\tag {1}\int_a^ {g (x)} f (t)\,dt,$$ you would find the derivative using the chain rule. As stated above, the basic differentiation rule for integrals is: