*Đặt
$t=\sqrt[3]{3x+1}\Rightarrow x=\frac{t^3-1}{3}\Rightarrow dx=t^2dt$
$I_1=\frac{1}{3}\int\limits_1^2
t^4dt=\frac{1}{15}t^5|^2_1=\frac{31}{15}$
*$I_2= (\frac{4}{\ln10}
10^{\frac{x}{4}}+\frac{1}{\pi}\cos\pi x)|^2_{-2}$
$\Rightarrow
I_2=\frac{36}{\sqrt{10}\ln10}$