Question

Q. Intigrate
ʃ1/(1-x)3dx

Answer 1

Answer on Question #53155 – Math – Integral Calculus

Evaluate the following integral: $\int \frac{1}{(1 - x)^3} dx$

Solution

Let's compute the integral:

$$\begin{array}{l} \int \frac {1}{(1 - x) ^ {3}} d x = - \int \frac {- d x}{(1 - x) ^ {3}} = - \int \frac {d (- x)}{(1 - x) ^ {3}} = - \int (1 - x) ^ {- 3} d (1 - x) = | t = 1 - x | = - \int t ^ {- 3} d t = - \frac {t ^ {- 2}}{- 2} + C = \\ = - \frac {(1 - x) ^ {- 2}}{- 2} + C = \frac {1}{2 (1 - x) ^ {2}} + C, \end{array}$$

where $C$ is an arbitrary real constant.

Answer: $\int \frac{1}{(1 - x)^3} dx = \frac{1}{2(1 - x)^2} + C$ .

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