[tex]\int_{0}^{\frac{sqrt{3}}{2}}\frac{2x^5 + x^3}{sqrt{4x^2 +1} }dx[/tex]
[TEX]t=\sqrt{4x^2+1}\right t^2=4x^2+1\righ \frac{1}{4}tdt=xdx[/TEX]
Đổi cận : [TEX]\left{x=0\righ t=1\\x=\frac{\sqrt{3}}{2}\righ t=2[/TEX]
[TEX]I=\frac{1}{2}\int_{0}^{2}\frac{\( \frac{t^2-1}{4} \)^2.tdt}{t}+\frac{1}{4}\int_{0}^{2}\frac{\( \frac{t^2-1}{4}\)tdt}{t}[/TEX]
[TEX]=\frac{1}{32}\int_{0}^{2}(t^4-2t^2+1)dt+\frac{1}{64}\int_{0}^{2}(t^2-1)dt=OK^n[/TEX]