Quien me podría ayudar a resolver esta integral triple?

(1) Primero resolvamos la siguiente integral<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI_z%3D%5Cint_%7B%5Csqrt%7B1-x%5E2-y%5E2%7D%7D%5E%7B%5Csqrt%7B2xy%7D%7D%5Cdfrac%7Bz%7D%7Bx%5E2%2By%5E2%2Bz%5E2%7D~dz%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctext%7BEn%20este%20caso%20debemos%20observar%20a%20%24x%5E2%2By%5E2%24%20como%20si%20fuese%20una%20%24constante%24%7D%5C%5C%20%5C%5C%20%5C%5C%0AI_z%3D%5Cdfrac%7B1%7D%7B2%7D%5Cint_%7B%5Csqrt%7B1-x%5E2-y%5E2%7D%7D%5E%7B%5Csqrt%7B2xy%7D%7D%5Cdfrac%7B%5Cpartial_z%28x%5E2%2By%5E2%2Bz%5E2%29%7D%7Bx%5E2%2By%5E2%2Bz%5E2%7D~dz%5C%5C%20%5C%5C%20%5C%5C%0AI_z%3D%5Cdfrac%7B1%7D%7B2%7D%5Cleft.%5Cln%5Cleft%7Cx%5E2%2By%5E2%2Bz%5E2%5Cright%7C%5Cright%7C_%7Bz%3D%5Csqrt%7B1-x%5E2-y%5E2%7D%7D%5E%7Bz%3D%5Csqrt%7B2xy%7D%7D%5C%5C%20%5C%5C%20%5C%5C%0AI_z%3D%5Cdfrac%7B1%7D%7B2%7D%5Cln%7Cx%5E2%2By%5E2%2B2xy%7C-%5Cdfrac%7B1%7D%7B2%7D%5Cln%201%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7BI_z%3D%5Cln%7Cx%2By%7C%7D" />

(2) Hasta aquí tenemos que resolver<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI%3D%5Cint_%7B1%7D%5E%7B2%7D%5Cint_%7Bx%7D%5E%7B2x%7D%5Cln%7Cx%2By%7C%20~dy~dx%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctext%7BEntonces%20calculemos%20antes%20la%20siguiente%20integral%7D%3A%5C%5C%20%5C%5C%0AI_y%3D%5Cint_%7Bx%7D%5E%7B2x%7D%5Cln%7Cx%2By%7C~dy%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctext%7BYa%20que%20%241%5Cleq%20x%5Cleq2%24%20entonces%20esta%20integral%20se%20reduce%20a%7D%5C%5C%20%5C%5C%0AI_y%3D%5Cint_%7Bx%7D%5E%7B2x%7D%5Cln%28x%2By%29~dy%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctext%7BIntegraci%5C%27on%20por%20partes%3A%20%7D%5C%5C%20%5C%5C%20%20I_y%3D%5Cleft.%5By%5Cln%28x%2By%29%5D~%5Cright%7C_%7By%3Dx%7D%5E%7By%3D2x%7D-%5Cint_%7Bx%7D%5E%7B2x%7D%20y~%5B%5Cpartial_y%20%5Cln%28x%2By%29%5D~dy%5C%5C%20%5C%5C%20%5C%5C" /><img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI_y%3D%5B2x%5Cln%283x%29-x%5Cln%282x%29%5D-%5Cint_%7Bx%7D%5E%7B2x%7D%5Cdfrac%7By%7D%7Bx%2By%7D~dy%5C%5C%20%5C%5C%20%5C%5C%0AI_y%3D%5B2%5Cln%283x%29-%5Cln%282x%29%5Dx-%5Cint_%7Bx%7D%5E%7B2x%7D1-%5Cdfrac%7Bx%7D%7Bx%2By%7D~dy%5C%5C%20%5C%5C%20%5C%5C%0AI_y%3Dx%5Cln%28%5Cfrac%7B9%7D%7B2%7Dx%29-x%2B%5Cint_%7Bx%7D%5E%7B2x%7D%5Cdfrac%7Bx%7D%7Bx%2By%7D~dy%5C%5C%20%5C%5C%20%5C%5C%0AI_y%3Dx%5Cln%28%5Cfrac%7B9%7D%7B2%7Dx%29-x%2Bx%5Cint_%7Bx%7D%5E%7B2x%7D%5Cdfrac%7B1%7D%7Bx%2By%7D~dy%5C%5C%20%5C%5C%20%5C%5C%0AI_y%3Dx%5Cln%28%5Cfrac%7B9%7D%7B2%7Dx%29-x%2Bx%5Cleft.%5B%5Cln%28x%2By%29%5D~%5Cright%7C_%7By%3Dx%7D%5E%7By%3D2x%7D%5C%5C%20%5C%5C%20%5C%5C%0AI_y%3Dx%5Cln%28%5Cfrac%7B9%7D%7B2%7Dx%29-x%2Bx%5B%5Cln%283x%29-%5Cln%282x%29%5D%5C%5C%20%5C%5C%20%5C%5C%0AI_y%3Dx%5Cln%28%5Cfrac%7B9%7D%7B2%7Dx%29-x%2Bx%5Cln%5Cfrac%7B3%7D%7B2%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7BI_y%3Dx%5Cln%28%5Cfrac%7B27%7D%7B4%7Dx%29-x%7D" />(3) Luego tenemos<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI%3D%5Cint_%7B1%7D%5E%7B2%7D%20x%5Cln%5Cleft%28%5Cfrac%7B27%7D%7B4%7Dx%5Cright%29-x~dx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cint_%7B1%7D%5E%7B2%7D%20x%5Cln%5Cleft%28%5Cfrac%7B27%7D%7B4%7Dx%5Cright%29~dx-%5Cfrac%7B3%7D%7B2%7D%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cln%5Cfrac%7B27%7D%7B4%7D%20%5Cint_%7B1%7D%5E%7B2%7D%20x~dx%20%2B%5Cint_%7B1%7D%5E%7B2%7Dx%5Cln%20x~dx-%5Cfrac%7B3%7D%7B2%7D%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cfrac%7B3%7D%7B2%7D%5Cln%5Cfrac%7B27%7D%7B4%7D%20%2B%5Cint_%7B1%7D%5E%7B2%7Dx%5Cln%20x~dx-%5Cfrac%7B3%7D%7B2%7D%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cfrac%7B3%7D%7B2%7D%5Cln%5Cfrac%7B27%7D%7B4%7D%20%2B%5Cln4-%5Cfrac%7B3%7D%7B4%7D-%5Cfrac%7B3%7D%7B2%7D%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cln%5Cleft%28%5Cfrac%7B3%5E%7B9%2F2%7D%7D%7B2%5E3%7D%5Ccdot%202%5E2%5Cright%29-%5Cfrac%7B9%7D%7B4%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7B%5Cboxed%7BI%3D%5Cln%5Cfrac%7B81%5Csqrt3%7D%7B2%7D-%5Cfrac%7B9%7D%7B4%7D%7D%7D" />.