Integral using Substitution (Polynomials and Rationals)

I = \int \frac{9}{{(81 x - 2)}^{4}} d x

Put u = 81 x - 2, then

d u = (81) d x

or, (\frac{1}{9}) d u = (9) d x

I = \int {(u)}^{-4} (\frac{1}{9}) d u

I = \frac{1}{9} \int {(u)}^{-4} d u

I = \frac{1}{9} \frac{{(u)}^{-3}}{-3} + C

I = \frac{1}{9} \frac{-1}{3 {(u)}^{3}} + C

I = \frac{-1}{27 {(81 x - 2)}^{3}} + C

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