Integral using Substitution (Polynomials and Rationals)

I = \int {(2 x^{3} - 21 x + 2)}^{2} (-2 x^{2} + 7) d x

Put u = 2 x^{3} - 21 x + 2, then

d u = (6 x^{2} - 21) d x

or, (\frac{-1}{3}) d u = (-2 x^{2} + 7) d x

I = \int {(u)}^{2} (\frac{-1}{3}) d u

I = \frac{-1}{3} \int {(u)}^{2} d u

I = \frac{-1}{3} \frac{{(u)}^{3}}{3} + C

I = \frac{- {(2 x^{3} - 21 x + 2)}^{3}}{9} + C

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