Calculus help!! integral

integral of
(7x^2 +8x +128)/(x^3 +64x)

∫ (7x^2 +8x +128)/(x^3 +64x) dx

= ∫ (7x^2 +8x +128)/ [x*(x^2 + 64)] dx

We integrate this by partial fractions.

(7x^2 +8x +128) / [x*(x^2 + 64)] = A/x + (Bx + C)/(x^2 + 64)
7x^2 +8x +128 = A(x^2 + 64) + (Bx + C)x

If x = 0,
128 = 64A
A = 2

7x^2 +8x +128 = 2(x^2 + 64) + (Bx + C)x
7x^2 +8x +128 = 2x^2 + 128 + Bx^2 + Cx
7x^2 +8x +128 = (2+B)x^2 + Cx + 128
7 = 2+B
B = 5
C = 8

∫ (7x^2 +8x +128)/ [x*(x^2 + 64)] dx
= ∫ [2/x + (5x + 8)/(x^2 + 64)] dx
= 2 ∫ dx/x + ∫ (5x + 8)/(x^2 + 64)] dx
= 2 ∫ dx/x + 5∫ x/(x^2 + 64)] dx + 8∫ 1/(x^2 + 64)] dx

Let u = x^2 + 64
du = 2x dx
du/2 = x dx

= 2 ∫ dx/x + 5∫ 1/u du/2 + 8∫ 1/(x^2 + 64)] dx
= 2 ln |x| + 5/2 ln |x^2 + 64| + 8 *1/8 arctan x/8
= 2 ln |x| + 5/2 ln |x^2 + 64| + arctan x/8