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First we take the derivative of the vector using the product rule
Now we will find the magnitude of the result
We begin by squaring the i terms.
And now we square the j terms.
Now squaring the k terms give
Now we add all three results and use the identity
now we integrate the result
now we isolate for t.
And finally we plug this result into the original equation.
But that's ugly and hard to read so here's the ln of the result