Asked by Carly
Integrate (1/2)^(3x+2)dx using substitution.
Answers
Answered by
Reiny
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
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
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