Cho hàm số y=f(x) thỏa mãn $\Large\mathrm{f^{\prime}(x) . f(x)=x^{4}+x

Cho hàm số y=f(x) thỏa mãn $\Large\mathrm{f^{\prime}(x) . f(x)=x^{4}+x^{2} . }$ Biết f(0)=2 .Tính $\Large\mathrm{f^{2}(2) }$.

• A. $\Large\mathrm{f^{2}(2)=\dfrac{313}{15}}$
• B. $\Large\mathrm{f^{2}(2)=\dfrac{332}{15}}$
• C. $\Large\mathrm{f^{2}(2)=\dfrac{324}{15}}$
• D. $\Large\mathrm{f^{2}(2)=\dfrac{323}{15}}$

$\Large\mathrm{f^{\prime}(x) . f(x)=x^{4}+x^{2} \Rightarrow \int\limits_{0}^{2} f^{\prime}(x) . f(x) d x=\int\limits_{0}^{2}\left(x^{4}+x^{2}\right) d x }$

$\Large \Leftrightarrow \mathrm{ \int\limits_{0}^{2}f(x)d\left(f(x)\right)=\dfrac{136}{15}\Rightarrow \dfrac{f^2(x)}{2}\bigg|_0^2}=\dfrac{136}{15}$

$\Large \mathrm{ \dfrac{f^2(2)-4}{2}=\dfrac{136}{15}\Leftrightarrow f^2(x)=\dfrac{332}{15}}$