How to prove the below equality?

We have
I=
∫
ℝ
3
∣x∣
‾
‾
‾
√
e
−3∣x−2∣
dx
I=∫R3∣x∣e−3∣x−2∣dx
How to prove the following?
I=
∫
+∞
0
3
x+2
‾
‾
‾
‾
‾
√
e
−3x
dx+
∫
+∞
0
3
∣2−x∣
‾
‾
‾
‾
‾
‾
√
e
−3x
dx
I=∫0+∞3x+2e−3xdx+∫0+∞3∣2−x∣e−3xdx

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