Ответ:

[tex]f(x) = {e}^{4x} + \frac{1}{ \sin^{2} (7x) } [/tex]

[tex]f(x) = {e}^{kx} \: \: = > \: \: F(x) = \frac{1}{k} \times {e}^{kx} + C[/tex]

[tex]f(x) = \frac{1}{ \sin^{2} (kx) } \: \: = > \: \: F(x) = \frac{1}{k} \times ( - \cot(kx) ) + C[/tex]

[tex]F = \frac{1}{4} \times {e}^{4x} - \frac{1}{7} \times \cot(7x )= \frac{ {e}^{4x} }{4} - \frac{ \cot(7x) }{7} + C[/tex]