Integral using Substitution (Polynomials and Rationals)

I = \int \frac{-8 x^{2} + 3}{{(-56 x^{3} + 63 x - 6)}^{2}} d x

Put u = -56 x^{3} + 63 x - 6, then

d u = (-168 x^{2} + 63) d x

or, (\frac{1}{21}) d u = (-8 x^{2} + 3) d x

I = \int {(u)}^{-2} (\frac{1}{21}) d u

I = \frac{1}{21} \int {(u)}^{-2} d u

I = \frac{1}{21} \frac{{(u)}^{-1}}{-1} + C

I = \frac{1}{21} \frac{-1}{{(u)}^{1}} + C

I = \frac{-1}{21 (-56 x^{3} + 63 x - 6)} + C

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