Integral using Substitution (Polynomials and Rationals)

I = \int \frac{- x + 4}{(- x^{2} + 8 x - 2)} d x

Put u = - x^{2} + 8 x - 2, then

d u = (-2 x + 8) d x

or, (\frac{1}{2}) d u = (- x + 4) d x

I = \int \frac{1}{(u)} (\frac{1}{2}) d u

I = \frac{1}{2} \int \frac{1}{(u)} d u

I = \frac{1}{2} l n (u)

I = \frac{1}{2} l n (- x^{2} + 8 x - 2) + C

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Copyright © Dayal D. Purohit, Ph.D.(Mathematics)