Monkey Raptor V.2

Hi. 👋 We want to find the solution for the indefinite integral from: $∫ (\ln x)\ dx$ $∫ 1/(\ln x)\ dx$ $∫ 1/(x.\ln x)\ dx$ $∫ 1/(x^{2}.\ln x)\ dx$ We need to keep in mind that: $∫ 1/x\ dx = \ln |x| +\ C$ Well, that's a definition. Right then. To solve each of those, we may employ one of these methods: Integral by parts ⬇️ $∫ u.dv = u.v - ∫ v.du$ Substitution of $1/u$ ⬇️ $∫ 1/{u}\ du = \ln u +\ C$ Using integral table look-up, or probably remembering bits from integral table. First Problem $∫ (\ln x)\ dx$ The solution can be achieved using integral by parts. u = ln x dv = dx du/dx [derivative of u] = 1/x switch the (dx) to right side ► du = (1/x) dx v [integral of dv ► ∫ 1 dx] = x Substitute those variables: ∫ u.dv = u.v - ∫ v.du ∫ (ln x) dx = (ln x).x - ∫ x.(1/...

A fun time — in mathematics. This one sophism is using integral and it is taken from Mudd Math Fun Facts — the calculation ends up with 0 = 1 . The link is also gone now, as they revamped the website. Sophism means a fallacious argument, especially one used deliberately to deceive. Sophisticate originates from sophisticus (Mediaeval Latin), while sophism is from Greek sophisma — different origins, but lo! Sophism and sophisticate, both have sophis . And yes, sophism has its sophistication. Quoted Consider the following integral: ∫(1/x) dx -------------------------------------------------- Perform integration by parts: Let u = 1/x dv = dx du = -1/x² dx v = x -------------------------------------------------- Then obtain: ∫(1/x) dx = (1/x).x - ∫x(-1/x²) dx = 1 + ∫(1/x) dx ❓ Let's continue the last line: $∫{1/x} dx = 1 + ∫{1/x} dx$ Subtract both sides with $∫{1/x} dx$. $∫{1/x} dx - ∫{1/x} dx = 1 + ∫{1/...

First of all, of course, 1 ≠ 0 . One is not zero. If they were similar, blimey! Imagine how the bridge construction would be and how many of us would chew beams . The steps: chair ≠ banana Counterexample: Bob ate a chair yesterday. Hi, Bob. It's your boardroom meeting suggestion which led to the two-layer right-click menu in Windows 11, innit? 🤔 Or was it meating? Let's dissect the proof from Mudd Math Fun Facts which yields 1 = 0 — the link is gone now. 😂 Quoted A bit paraphrased. Consider two non-zero numbers x and y such that: x = y ------------------------------------------------------------ Then x² = xy (multiplied by x) Subtract both sides with y²: x² - y² = xy - y² ------------------------------------------------------------ Divide by (x-y), we obtain: x + y = y Since x = y, we see that: 2y = y ------------------------------------------------------------ Thus 2 = 1 (divided by y), since we started with nonzero y. -----------...