For $f(x)=x \sin (4 x)$ , find a function $F(x)$ such that $F^{\prime}(x)=f(x)$ and $F(0)=0$ .
A) $\frac{1}{4} x \cos (4 x)-\frac{1}{4} \sin (4 x)$
B) $-\frac{1}{4} x \cos (4 x)+\frac{1}{4} \sin (4 x)$
C) $\frac{1}{4} x \cos (4 x)-\frac{1}{16} \sin (4 x)$
D) $-\frac{1}{4} x \cos (4 x)+\frac{1}{16} \sin (4 x)$

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The Answer of For $f(x)=x \sin (4 x)$ , find a function $F(x)$ such that $F^{\prime}(x)=f(x)$ and $F(0)=0$ .
A) $\frac{1}{4} x \cos (4 x)-\frac{1}{4} \sin (4 x)$
B) $-\frac{1}{4} x \cos (4 x)+\frac{1}{4} \sin (4 x)$
C) $\frac{1}{4} x \cos (4 x)-\frac{1}{16} \sin (4 x)$
D) $-\frac{1}{4} x \cos (4 x)+\frac{1}{16} \sin (4 x)$

For f(x)=xsin⁡(4x)f(x)=x \sin (4 x)f(x)=xsin(4x) , Find a Function F(x)F(x)F(x) Such That F′(x)=f(x)F^{\prime}(x)=f(x)F′(x)=f(x)

For $f(x)=x \sin (4 x)$ , Find a Function $F(x)$ Such That $F^{\prime}(x)=f(x)$