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.
Integration by parts is a technique used in calculus to evaluate the integral of a product of two functions. It involves breaking down the product into two separate parts and using a specific formula to simplify the integral.
Integration by parts is typically used when the integral being evaluated is in the form of a product, and the integrand (the function inside the integral) cannot be easily integrated using other techniques such as substitution or trigonometric identities.
To perform integration by parts, you must first identify which part of the integrand will be the "u" term and which part will be the "dv" term. Then, using the formula: ∫udv = uv - ∫vdu, you can simplify the integral and solve for the original integral.
Integration by parts allows for the evaluation of integrals that would otherwise be difficult or impossible to solve. It also allows for the integration of more complex functions, making it a valuable tool in calculus and other areas of mathematics and science.
Integration by parts is not always applicable and may not always lead to a solution. It also requires careful selection of the "u" and "dv" terms, which can be challenging in some cases. Additionally, integration by parts may result in a more complex integral that is not easily solvable.