You should have told us so explicitly. Use integration by parts here, denote u=ln(3x-2). Find v and du, and then you'll have to integrate 3x/(3x-2) which you should do by first simplifying the expression by polynomial long division. And are you sure the answer doesn't have absolute signs? There is a ln in the answer is there not?darthxepher said:I tried but it said the answer doesn't involve absolute value... :( the original problem was find the integral of >>> ln(3x-2)
Yeah, but look heredarthxepher said:But wait i asked to integrate (3x)/(3x-2) not dx/(3x-2)... hm... I am confused
Integration by parts is a mathematical technique used to evaluate integrals that are products of two functions. It involves breaking down the integral into smaller parts and using the product rule of differentiation to solve it.
Integration by parts works by using the product rule of differentiation to simplify the integral into a more manageable form. The formula for integration by parts is ∫u dv = uv - ∫v du, where u and v are two functions and du and dv are their respective differentials.
The natural log function, denoted as ln(x), is the inverse of the exponential function. It is a logarithmic function with a base of e, where e is a mathematical constant approximately equal to 2.718. The natural log function is commonly used in mathematics, especially in calculus and logarithmic differentiation.
Integration by parts can help solve natural log integrals by breaking down the integral into two parts and using the product rule of differentiation. This allows for the integral to be simplified and solved using known integration techniques.
It is important to use integration by parts when dealing with natural log integrals because they can be difficult to solve using other integration techniques. Integration by parts provides a systematic way to simplify the integral and make it easier to solve. It is also useful when dealing with more complex integrals that involve natural log and other functions.