u = 4x^2 - 6x + 7
du = (8x - 6)dx = 2(4x - 3)dx
∫((4x - 3)/(4x^2 - 6x + 7)^4)dx
= (1/2)∫du/(u^4)
= (1/2)(-1/(3u^3)) + C
= -1/(6u^3) + C
= -1/(6(4x^2 - 6x + 7)^3) + C.
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Verified answer
u = 4x^2 - 6x + 7
du = (8x - 6)dx = 2(4x - 3)dx
∫((4x - 3)/(4x^2 - 6x + 7)^4)dx
= (1/2)∫du/(u^4)
= (1/2)(-1/(3u^3)) + C
= -1/(6u^3) + C
= -1/(6(4x^2 - 6x + 7)^3) + C.