Have functions fn(x)=ln^n(x) and F(x)=xlnx+ax+b. What are a,b if F is primitive pf f?
You should consider n=1 such that:
`f_1(x) = ln x`
You need to remember that a primitive of a function is that function F(x) that differentiated yields f(x) such that:
`F'(x) = f(x)`
You need to differentiate F(x) with respect to x such that:
`F'(x) = x'*ln x + x*(ln x)' + (ax)' + b'`
`F'(x) = ln x + x*(1/x) + a`
`F'(x) = ln x + 1 + a`
Using the definition of primitive yields:
`F'(x) = f(x) =gt ln x + 1 + a = ln x =gt a + 1 = 0 =gt a = -1`
Notice that b may have any real value such that: `b in R`
Hence, evaluating a and b under given conditions yields `a = -1` and `b in R` .