Question

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Answer 1

F(x)=-2sin0,4x/0,4+2^x*ln8/ln2+C=-5sin0,4x+2^x*3ln2/ln2+C=
=-5sin0,4x+3*2^x+C

Answer 2

f(x)=-2cos0.4x+2ˣln8
F(x)=∫(-2cos0.4x+2ˣln8)dx=-2∫cos0.4xdx+ln8∫2ˣdx
-2∫cos0.4xdx ={0.4x=z  0.4dx=dz  dx=dz/0.4}=-2/0.4*∫cosz=-5sin0.4x
ln8∫2ˣdx=ln8*2ˣ/ln2=ln8/ln2*2ˣ=3ln2/ln2*2ˣ=3*2ˣ
F(x)=-5sin0.4x+3*2ˣ+C