Integral using Substitution (Polynomials and Rationals)

I = \int \frac{-3 x^{2} - 8 x - 3}{{(- x^{3} - 4 x^{2} - 3 x - 1)}^{3}} d x

Put u = - x^{3} - 4 x^{2} - 3 x - 1, then

d u = (-3 x^{2} - 8 x - 3) d x

or, d u = (-3 x^{2} - 8 x - 3) d x

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

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

I = \frac{{(u)}^{-2}}{-2} + C

I = \frac{-1}{2 {(u)}^{2}} + C

I = \frac{-1}{2 {(- x^{3} - 4 x^{2} - 3 x - 1)}^{2}} + C

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