The integral: \frac{dx}{(4x^2-24x+27)^\frac{3}{2}}

Harlen Pritchard

Harlen Pritchard

Answered question

2020-11-23

The integral: dx(4x224x+27)32

Answer & Explanation

brawnyN

brawnyN

Skilled2020-11-24Added 91 answers

4x224x+27=(2x6)232
let 2x-6 = t then 2dx = dt
so,
1(4x224x+27)32dx=121(t232)32dt
now we use the integration formula
1(u2a2)32du=ua2u2a2+C
121(t232)32dt=t18t29+C
Then,
1(4x224x+27)32dx=62x184x224x+27+C=3x94x224x+27+C

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