Mathematics

Solve
$$\int {{x^{ - 3}}\left( {x + 1} \right)dx} $$


SOLUTION
$$\int \frac{x+1}{^3}.dx$$

$$=\int [\frac{1}{x^2}+\frac{1}{x^3}]dx$$

$$=\int \frac{1}{x^2}.dx+\int \frac{1}{x^3}.dx$$

$$=\frac{x^{-2+1}}{-2+1}+\frac{x^{-3+1}}{-3+1}+c$$

$$=-\frac{1}{x}-\frac{1}{2x^2}+c$$

$$=-\frac{1}{x}-\frac{1}{2x^2}+c$$
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Subjective Medium Published on 17th 09, 2020
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