Thus,
2x-1

(2x2-2x+5)3
dx
=
2x-1

u3
1

2(2x-1)
du
(substituting for u and dx)
=
1

2u3
du
(canceling the term (2x-1))
=
1

2
u3du
(integrand in exponent form)
=
1

2
u3du
(slip the constant outside)
=
1

2
u2

-2
+ C
(evaluate the integral)
=
-
1

4u2
+ C
(simplify)
=
-
1

4(2x2-2x+5)2
+ C
(substitute back)


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