Hello,
I just need quick help on recognizing why we need to use Integration by Parts. I know it's when there's a product of two different functions when integrating, but what is the two different functions in this equation?
\(\displaystyle \int k\ln(t)dt\)
\(\displaystyle k\int \ln(t)dt\) Factored K outside integrand
Letter 'k' is a constant in this case. So how do we recognize to use Integration by Parts here? \(\displaystyle Ln\) is natural log which is one function, is the other function the \(\displaystyle t\) inside the natural log? Making it a product of two different functions? If this is the case, would we let \(\displaystyle u = \ln(t)\), then \(\displaystyle du = \dfrac{1}{t} dt\) and \(\displaystyle dv = 1dt\) and \(\displaystyle v = t\)
Thank you.
I just need quick help on recognizing why we need to use Integration by Parts. I know it's when there's a product of two different functions when integrating, but what is the two different functions in this equation?
\(\displaystyle \int k\ln(t)dt\)
\(\displaystyle k\int \ln(t)dt\) Factored K outside integrand
Letter 'k' is a constant in this case. So how do we recognize to use Integration by Parts here? \(\displaystyle Ln\) is natural log which is one function, is the other function the \(\displaystyle t\) inside the natural log? Making it a product of two different functions? If this is the case, would we let \(\displaystyle u = \ln(t)\), then \(\displaystyle du = \dfrac{1}{t} dt\) and \(\displaystyle dv = 1dt\) and \(\displaystyle v = t\)
Thank you.