Integral using Substitution (Polynomials and Rationals)

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

Put u = x - 3, then

d u = (1) d x

or, (-1) d u = (-1) d x

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

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

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

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

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

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