Use integration by parts to evaluate the integral.

Integral from 1 to 7 sqrt(t)*(lnt) dt

d=ln(t)
du=1/t
dv=t^(1/2)
v=2/3*t^(3/2)

2/3*ln(t)*(1/t)-integral(t^(-1)*2/3*t^…
2/3*ln(t)*(1/t)-(2/3)(2/3)t^(3/2)
2/3*t^(3/2)(ln(t)-2/3) evaluated from 1 to 7. i'm sure you can do the evaluation