Integral of 1x2\frac{1}{x^{2}}

The calculator will find the integral/antiderivative of 1x2\frac{1}{x^{2}}, with steps shown.

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Your Input

Find 1x2dx\int \frac{1}{x^{2}}\, dx.

Solution

Apply the power rule xndx=xn+1n+1\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1} (n1)\left(n \neq -1 \right) with n=2n=-2:

1x2dx=x2dx=x2+12+1=(x1)=(1x){\color{red}{\int{\frac{1}{x^{2}} d x}}}={\color{red}{\int{x^{-2} d x}}}={\color{red}{\frac{x^{-2 + 1}}{-2 + 1}}}={\color{red}{\left(- x^{-1}\right)}}={\color{red}{\left(- \frac{1}{x}\right)}}

Therefore,

1x2dx=1x\int{\frac{1}{x^{2}} d x} = - \frac{1}{x}

Add the constant of integration:

1x2dx=1x+C\int{\frac{1}{x^{2}} d x} = - \frac{1}{x}+C

Answer: 1x2dx=1x+C\int{\frac{1}{x^{2}} d x}=- \frac{1}{x}+C