1. ∫x³/(4+x²)^(3/2) dx
= ∫x[(x²+4)-4]/(4+x²)^(3/2) dx
= ∫[x(4+x²)^(-1/2) - 4x(x²+4)^(-3/2)] dx
= ∫x(4+x²)^(-1/2)dx - 4∫x(x²+4)^(-3/2)dx
= 1/2∫(4+x²)^(-1/2)d(4+x²) - 4(1/2)∫(x²+4)^(-3/2)d(x²+4)
= (4+x²)^(1/2) +4 (x²+4)^(-1/2) + C
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