Let I n = x n dx/x 2 + 1. (a) Prove that In = x n1
Question:
Let In = xn dx/x2 + 1.
(a) Prove that In = xn−1 − 1 − In−2.
(b) Use (a) to calculate In for 0 ≤ n ≤ 5.
(c) Show that, in general,
Transcribed Image Text:
12n+1 = 12n = x²n 2n x2n-2 2n - 2 12 + (−1)²-¹ + (−1)¹¹1 In(x² + 1) + C 2 x2n-1 x2n-3 2n - 1 2n-3 + (-1)"¹x + (-1)" tan¹ x + C
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a I dx fx1 dx xdx S x 1 b First compute Io and I directly 12 x dx dx Io 1 21 tanxC and ...View the full answer
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