Verified answer

a. ∫(4x⁻³-5sinx-7)dx=∫(4/x³-5sinx-7)dx=4∫1/x³*dx-5∫sindx-7∫1dx=-(2/x²)+5cosx-7x+C

b. ∫(z³dz)/(⁴√(5z⁴-3)³)=1/20*∫1/(⁴√u³)*du=1/20*∫1/u^(3/4)*du=(⁴√u)/5+C=1/5*⁴√(5z⁴-3)+C

u=5z⁴-3

du=20z³dz