The trick here is to use an appropriate substitution. Let u=a^3.
Then du/da=3a^2, and du=3a^2da.
We can now make two key substitutions: In (3a^2)da/(1+a^6), replace 3a^2 by du and a^6 by u^2.
Then we have the integral of du/(1+u^2).
Integrating, we get arctan u + c. Substituting a^3 for u, the final result (the integral in question) is arctan a^3 + c.
Check this by differentiation. if you find the derivative with respect to a of arctan a^3 + c, you MUST obtain the result 3a^2/(1+a^6).
52488 because 9 times 9 is 81, 81 times 9 equals 729, 729 times 9 equals 6561. 6561 x 8 = 52488
Its postive and ill help u with more if you actually mark brainly
The recursive formula of the geometric sequence is given by option D; an = (1) × (5)^(n - 1) for n ≥ 1
<h3>How to determine recursive formula of a geometric sequence?</h3>
Given: 1, 5, 25, 125, 625, ...
= 5
an = a × r^(n - 1)
= 1 × 5^(n - 1)
an = (1) × (5)^(n - 1) for n ≥ 1
Learn more about recursive formula of geometric sequence:
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