Integral using Substitution (Polynomials and Rationals)

I = \int \frac{-6 x^{2} - 7 x + 6}{(-12 x^{3} - 21 x^{2} + 36 x - 2)} d x

Put u = -12 x^{3} - 21 x^{2} + 36 x - 2, then

d u = (-36 x^{2} - 42 x + 36) d x

or, (\frac{1}{6}) d u = (-6 x^{2} - 7 x + 6) d x

I = \int \frac{1}{(u)} (\frac{1}{6}) d u

I = \frac{1}{6} \int \frac{1}{(u)} d u

I = \frac{1}{6} l n (u)

I = \frac{1}{6} l n (-12 x^{3} - 21 x^{2} + 36 x - 2) + C

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