Mar 23, 2026 · Encountering the integral $$ \\int \\frac{x^2-2}{\\left(x^2+2\\right) \\sqrt{x^4+4}} d x, $$ from MIT integration 2026 Semifinal , I tried my best to finish it within the time limit. $$ …

Jan 4, 2026 · The other kind of integral you often encounter is the definite integral. This is the integral that is sometimes described as "the area under the curve" (although I would consider that an …

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.

Nov 29, 2013 · Wolfram Mathworld says that an indefinite integral is "also called an antiderivative". This MIT page says, "The more common name for the antiderivative is the indefinite integral." One is free …

Feb 6, 2026 · Evaluate an integral involving a series and product in the denominator Ask Question Asked 1 month ago Modified 1 month ago

Dec 23, 2010 · One is the question of why the definite Riemann integral gives the correct notion of "area under a curve" for a (nonnegative, Riemann integrable) function. The other, which seems to be what …

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 functions …

Dec 15, 2017 · A different type of integral, if you want to call it an integral, is a "path integral". These are actually defined by a "normal" integral (such as a Riemann integral), but path integrals do not seek to …

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 in a form o...

Mar 17, 2015 · A different approach, building up from first principles, without using cos or sin to get the identity, $$\arcsin (x) = \int\frac1 {\sqrt {1-x^2}}dx$$ where the integrals is from 0 to z. With the …