dx(t)=24cos(8t)

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Solution for dx(t)=24cos(8t) equation: 


Simplifying
dx(t) = 24cos(8t)

Multiply dx * t
dtx = 24cos(8t)

Remove parenthesis around (8t)
dtx = 24cos * 8t

Reorder the terms for easier multiplication:
dtx = 24 * 8cos * t

Multiply 24 * 8
dtx = 192cos * t

Multiply cos * t
dtx = 192cost

Solving
dtx = 192cost

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Divide each side by 'tx'.
d = 192cosx-1

Simplifying
d = 192cosx-1

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