I need to know how to get the answers. Evaluate the indefinite integral int tan-

Question

I need to know how to get the answers.

Evaluate the indefinite integral int tan-1 (t2) dt as a power series. The MacLaurin series for tan-1 x = x - x3/3 + x5/5 - x7/7 + = (-1)n x2n + 1/2n + 1] Select the correct answer. C + (-1)n t4n + 3/(2n + 1)(4n + 3) C + (-1)n t4n + 3/(4n + 3) C + (-1)n t4n + 2/(2n +1)(4n + 3) C + (-1)n t2n + 2/(2n + 1) None of the above Find the first three nonzero terms in the MacLaurin series for the function f(x) = e-x2 cos 4x Select the correct answer. 1 - 17 x2 + 19.17 x4 1 - 9 x2 + 11.17 x4 1 - 9 x2 + 19.17 x4 1 - 9 x + 19.17 x2

Explanation / Answer

6. Sub t^2 for x to get sum (-1)^n t^2(2n+1)/(2n+1)= sum (-1)^n t^(4n+2)/(2n+1)

Take the antiderivative using the power rule. sum (-1)^n t^(4n+3)/(4n+3)(2n+1).

A)

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