Să se determine functiile [tex]f: D \rightarrow R[/tex], care au primitive de forma:

a) [tex]F(x)=x\left(\ln ^{2} x-\ln x^{2}+1\right)[/tex], [tex]\mathbf{x} \in(\mathbf{0},+\infty)[/tex]

b) [tex]F(x)=e^{x+1}\left(x^{2}-4 x\right), x \in \mathbb{R}[/tex]

c) [tex]F(x)=2 x \sin x+2 \cos x-x^{2}[/tex], [tex]\mathbf{x} \in \mathbf{R}[/tex];

d) [tex]F(x)=\frac{x}{2} \sqrt{9-x^{2}}+\frac{9}{2} \arcsin \frac{x}{3}[/tex], [tex]\mathbf{x} \in(-\mathbf{3}, \mathbf{3})[/tex]