Evaluate the integral. Please show your work. Thank you.?

Question

The integral (with lower limit 1 and upper limit 2) of x^4 (lnx)^2 dx.

Use Integration by parts to answer this question.

Answer 1

from the ⌠udv = uv - ⌠vdu, let u=(lnx)^2 and dv=x^4dx
hence du=2dx/x and v=x^5/5
substituing values we have:
x^4 (lnx)^2 dx = (lnx)^2(x^5/5) - ⌠(x^5/5)(2dx/x)
= (lnx)^2(x^5/5) - ⌠(2/5)x^4dx
= (lnx)^2(x^5/5) - x^5/10
then using the limits; this yields to 1.796442507

Answer 2

ans in 1.79644
used my calculator