Tìm nguyên hàm của hàm số(fleft( x right)={{x}^{3}}ln left( frac{4-{{x}^{2}}}{4+{{x}^{2}}} right)) ?

Đặt : (left{ begin{array}{l}
u = ln left( {frac{{4 – {x^2}}}{{4 + {x^2}}}} right)\
dv = {x^3}dx
end{array} right. Rightarrow left{ begin{array}{l}
du = frac{{16x}}{{{x^4} – 16}}\
v = frac{{{x^4}}}{4} – 4 = frac{{{x^4} – 16}}{4}
end{array} right.)

(Rightarrow int{{{x}^{4}}ln left( frac{4-{{x}^{2}}}{4+{{x}^{2}}} right)dx=left( frac{{{x}^{4}}-16}{4} right)ln left( frac{4-{{x}^{2}}}{4+{{x}^{2}}} right)-int{4xdx}=left( frac{{{x}^{4}}-16}{4} right)ln left( frac{4-{{x}^{2}}}{4+{{x}^{2}}} right)-2{{x}^{2}}}+C)