31.
\(F\left(x\right)=\int4^x.2^{2x+3}=\int8.16^xdx=\dfrac{8.16^x}{ln16}+C=\dfrac{2.16^x}{ln2}+C\)
\(F\left(0\right)=\dfrac{2}{ln2}\Leftrightarrow\dfrac{2}{ln2}+C=\dfrac{2}{ln2}\Leftrightarrow C=0\)
\(\Rightarrow F\left(x\right)=\dfrac{2.16^x}{ln2}\)
\(F\left(1\right)=\dfrac{32}{ln2}\Rightarrow A=32\)
32.
Đề họ in nhầm chỗ phương trình \(f\left(1\right)=5\), đúng ra phải là \(f\left(x\right)=5\)
\(f\left(x\right)=\int\left(2x+1\right)dx=x^2+x+C\)
\(f\left(1\right)=5\Rightarrow C=3\Rightarrow f\left(x\right)=x^2+x+3\)
\(x^2+x+3=5\Rightarrow x^2+x-2=0\Rightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)
\(S=log_21+log_22=1\)
