a)
[tex]f(x) = 2 - 3 {x}^{2} + 2x \\ F(x) = 2x - \frac{3 {x}^{2 + 1} }{2 + 1} + \frac{2x {}^{1 + 1} }{1 + 1} + C = 2x - {x}^{3} + {x}^{2} + C[/tex]
б)
[tex]f(x) = 4x + \sin(3x) \\ F(x) = \frac{4 {x}^{1 + 1} }{1 + 1} - \frac{ \cos(3x) }{3} + C = 2 {x}^{2} - \frac{1}{3} \cos(3x) + C[/tex]
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Answers & Comments
a)
[tex]f(x) = 2 - 3 {x}^{2} + 2x \\ F(x) = 2x - \frac{3 {x}^{2 + 1} }{2 + 1} + \frac{2x {}^{1 + 1} }{1 + 1} + C = 2x - {x}^{3} + {x}^{2} + C[/tex]
б)
[tex]f(x) = 4x + \sin(3x) \\ F(x) = \frac{4 {x}^{1 + 1} }{1 + 1} - \frac{ \cos(3x) }{3} + C = 2 {x}^{2} - \frac{1}{3} \cos(3x) + C[/tex]