Integral using Substitution (Polynomials and Rationals)

I = \int (-8 x^{2} + 12 x + 2) (8 x - 6) d x

Put u = -8 x^{2} + 12 x + 2, then

d u = (-16 x + 12) d x

or, (\frac{-1}{2}) d u = (8 x - 6) d x

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

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

I = \frac{-1}{2} \frac{{(u)}^{2}}{2} + C

I = \frac{- {(-8 x^{2} + 12 x + 2)}^{2}}{4} + C

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