evaluate : int(6x+5)^ 3/2 dx.
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Given : int(6x+5)^ 3/2 dx.
To Find : Evaluate
Solution:
∫(6x + 5)^ 3/2 dx
Let say y = 6x + 5
=> dy = 6dx
=> dx = dy/6
= ∫(y)^ 3/2 (dy/6)
= (1/6) ∫(y)^ 3/2 dy
∫xⁿ = xⁿ⁺¹/(n + 1) + C
= (1/6) y ^ 5/2 / ( 5/2) + C
= (1/15) ((6x + 5)^5/2 + C
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