Using the method of substitution, I=integral from 1 to 4 of x^2(1+3x^3)^3 dx= integral from a to b of f(u) du

Question

u= 1+3x^3

du= ? dx

a= 4

b= 193

f(u)= ?

Answer 1

u = 1 + 3x³

du = 9x²dx So, x²dx = (1/9)du

When x = 1, u = 4 = a

When x = 4, u = 1 + 3(4)³ = 193 = b

f(u) = (1/9)u³