The discussion revolves around the evaluation of an integral using integration by parts, specifically the integral of the form ∫xax. Participants are exploring the steps involved in the integration process and addressing potential errors in the calculations.
Participants are actively discussing the steps taken in the integration process, with some providing feedback on the correctness of the expressions. There is a recognition of different interpretations of logarithmic properties, and guidance is being offered without reaching a definitive conclusion.
There is a focus on ensuring the correct application of integration techniques and the handling of logarithmic expressions. Participants are navigating through potential misunderstandings related to the properties of logarithms and constants in integration.
The1337gamer said:Seems correct to me, you just need to evaluate the 2nd term, the integral, you know how to do integrate a^x as you've already done it, 1/ln(a) is just a constant.
The1337gamer said:It's the bottom line as:
2ln(a) = ln(a^2)
What you have is ln(a)ln(a) = (ln(a))^2.
The1337gamer said:xa^x - a^x/(2lna) isn't correct, xa^x - a^x/(ln(a))^2 is.