Detailed process of x ^ 2 / (x-1) ^ 10 DX for indefinite integral

X ^ 2 / (x-1) ^ 10 Description: x ^ 2 = (x-1 + 1) ^ 2 = (x-1) ^ 2 + 2 (x-1) + 1x ^ 2 / (x-1) ^ 10 = ((x-1) ^ 2 + 2 (x-1) + 1) / (x-1) ^ 10 = 1 / (x-1) ^ 8 + (2 (x-1) + 1) / (x-1) ^ 10 = (x-1) ^ (- 8) + 2 (x-1) ^ (- 9) + (x-1) ^ (- 10) original formula = ∫ [(x-1) ^ (- 8) + 2 (x-1) ^ (- 9) + (x-1) ^ (- 1) ^ -

Solving indefinite integral: ∫ ln (x ^ 2 + X + 10) DX

∫ ln (x ^ 2 + X + 10) DX = XLN (x ^ 2 + X + 10) - integral: XD (LN (x ^ 2 + X + 10) = XLN (x ^ 2 + X + 10) - integral: X (2x + 1) / (x ^ 2 + x + 10) DX = XLN (x ^ 2 + X + 10) - integral; [2 (x ^ 2 + X + 10) - (x + 20)] / (x ^ 2 + X + 10) DX = XLN (x ^ 2 + X + 10) - 2x + 1 / 2 integral: D (x ^ 2 + X + 10) / (x ^ 2 + X + 10) + 39

∫ X / (x ^ 2 + 4) DX for indefinite integral

Solution
∫x/(x²+4)dx
=1/2∫1/(x²+4)d(x²+4)
=1/2∫1/udu
=1/2ln|u|+C
=1/2ln(x²+4)+C

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