If ∫x⁵e⁴ˣ³dx = (1/48)e⁴ˣ³f(x) + C, where C is a constant of integration, then f(x) is equal to:

∫x⁵⋅e⁴ˣ³dx = (1/48)e⁴ˣ³f(x) + c
Put x³ = t
3x²dx = dt
∫x³⋅e⁴ˣ³⋅x²dx
(1/3)∫t⋅e⁴ᵗdt
(1/3)[t⋅e⁴ᵗ/4 - ∫e⁴ᵗ/4dt]
(1/3)[te⁴ᵗ/4 - e⁴ᵗ/16] + c
(1/48)[4te⁴ᵗ - e⁴ᵗ] + c
(1/48)[4x³e⁴ˣ³ - e⁴ˣ³] + c
∴f(x) = 4x³ - 1
From the given options (3) is most suitable