∫ (x-4)/x³ dx integrieren – Potenzgesetze, Verifikation & Fläche | Mathefrosch

Together we'll calculate the integral of (x−4)/x³ dx – entirely without substitution, using only the power rules. The fraction is split into x⁻² − 4x⁻³ and integrated using the power rule. Result: −1/x + 2/x² + C. Verification is achieved by differentiation and the definite integral from −2 to −1 (area = 2). Chapters: 0:00 Intro 1:09 Integration – Power Rules 2:05 Verification 2:32 Area The Math Frog shows you how it's done step by step. Subscribe for more integral calculus! Note about the voiceover: The voiceover in this video was partially created with an AI-generated version of my own voice. Therefore, some sentences may sound slightly off. Do you notice any unusual sentences? Feel free to write it in the comments so the clone can be improved. The Math Frog says thank you! #mathfrog #integralcalculus #integration #analysis #exponentiallaws #exponentialrule #antiderivative #math #mathematics