# Evaluate the integral. int(x^2-1)/(x^2)dx

Question
Applications of integrals
Evaluate the integral.
$$\displaystyle\int\frac{{{x}^{{2}}-{1}}}{{{x}^{{2}}}}{\left.{d}{x}\right.}$$

2020-11-10
Given That
$$\displaystyle\int\frac{{{x}^{{2}}-{1}}}{{{x}^{{2}}}}{\left.{d}{x}\right.}$$
$$\displaystyle=\int{\left({1}-\frac{{1}}{{x}^{{2}}}\right)}{\left.{d}{x}\right.}$$
$$\displaystyle=\int{\left.{d}{x}\right.}-\int\frac{{1}}{{{x}^{{2}}}}{\left.{d}{x}\right.}$$
$$\displaystyle={x}-{\left[\frac{{{x}^{{-{2}+{1}}}}}{{-{2}+{1}}}\right]}+{c}$$
$$\displaystyle={x}+\frac{{1}}{{x}}+{c}$$
$$\displaystyle\therefore\int\frac{{{x}^{{2}}-{1}}}{{{x}^{{2}}}}{\left.{d}{x}\right.}={x}+\frac{{1}}{{x}}+{c}$$

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