Question

Evaluate the function below from x = 1 up to x = 4.


∫(7−lnx(x)(3+lnx))dx

Answer 1

Suspicious of your typing, especially the lnx(x) part

Sent it to Wolfram and they read it as:
https://www.wolframalpha.com/input/?i=%E2%88%AB%287%E2%88%92lnx%28x%29%283%2Blnx%29%29dx+

https://www.wolframalpha.com/input/?i=%E2%88%AB%287%E2%88%92lnx%28x%29%283%2Blnx%29%29dx+%2C+from+1+to+4

Wolfram uses log for ln

Answer 2

To integrate lnx or x lnx, use integration by parts

u = lnx, du = 1/x dx
dv = dx, v = x
∫lnx dx = x lnx - ∫1/x * x dx = x lnx - x

If
u = lnx, du = 1/x dx
dv = x dx, v = 1/2 x^2
∫x lnx = 1/2 x^2 lnx - ∫1/2 x dx = 1/2 x^2 lnx - 1/4 x^2