Question

Integrate (1/2)^(3x+2)dx using substitution.

Answer 1

let u = 3x+2

du/dx = 3
du = 3dx
dx = (1/3)du

so integral (1/2)^(3x+2)dx
= integral (1/3)(1/2)^u du
= (1/3)/ln(1/2) (1/2)u +C
= (1/3)/ln(1/2) (1/2)^(3x+2) + C
or
= -1/3ln2 (1/2)^(3x+2) + C