Integral using Substitution (Polynomials and Rationals)

I = \int {(-12 x^{2} - 80 x - 1)}^{2} (3 x + 10) d x

Put u = -12 x^{2} - 80 x - 1, then

d u = (-24 x - 80) d x

or, (\frac{-1}{8}) d u = (3 x + 10) d x

I = \int {(u)}^{2} (\frac{-1}{8}) d u

I = \frac{-1}{8} \int {(u)}^{2} d u

I = \frac{-1}{8} \frac{{(u)}^{3}}{3} + C

I = \frac{- {(-12 x^{2} - 80 x - 1)}^{3}}{24} + C

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