I need help to solve the Fourier finite sine and cosine transforms:
First, reciprocal of derivative: $$ F_s\left(\frac{1}{\frac{\partial u}{\partial x}}\right)= \int_{0}^{a}\frac{1}{\frac{\partial u}{\partial x}}sin(\omega x) dx $$ $$ F_c\left(\frac{1}{\frac{\partial u}{\partial x}}\right)= \int_{0}^{a}\frac{1}{\frac{\partial u}{\partial x}}cos(\omega x) dx $$
Second, exponential of derivative: $$ F_s\left(e^\frac{\partial u}{\partial x}\right)= \int_{0}^{a}e^\frac{\partial u}{\partial x}sin(\omega x) dx $$ $$ F_c\left(e^\frac{\partial u}{\partial x}\right)= \int_{0}^{a}e^\frac{\partial u}{\partial x}cos(\omega x) dx $$