1.
F(z)=∫0zt+sintdt
F′(z)=z+sinz
∫x1t+sintdt=∫01t+sintdt−∫0xt+sintdt=F(1)−F(x)
dxd(F(1)−F(x))=F′(1)−F′(x)=1+sin1−x+sinx
2.
F(z)=∫0zsin4tdt
F′(z)=sin4z
∫2x3x+4sin4tdt=∫03x+4sin4tdt−∫02xsin4tdt=F(3x+4)−F(2x)
dxd(F(3x+4)−F(2x))=3F′(3x+4)−2F′(2x)=
=3sin4(3x+4)−2sin4(2x)
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