Take the integral of both sides of the equation ( ∫ ( ∑_k=0ⁿ n ⋅ k ⋅ xᵏ ) ⋅ (1 - x)ⁿ ). Explain what constant ( c ) you will need to take on the right-hand side to keep the equation valid.
a) ( c = 0 )
b) ( c = 1 )
c) ( c = n )
d) ( c = -n )