What is the integral of 1/((2x^2)) ?

The integral of 1/((2x^2)) is -1/(2x)+C

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integral of 1/((2x^2))

integral

\frac{1}{( 2 x ^{2} )}

- \frac{1}{2 x} + C

Solution steps

\int \frac{1}{2 x ^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{1}{x ^{2}} d x

Apply the Power Rule

= \frac{1}{2} (- \frac{1}{x})

Simplify

\frac{1}{2} (- \frac{1}{x}) : - \frac{1}{2 x}

= - \frac{1}{2 x}

Add a constant to the solution

= - \frac{1}{2 x} + C

in t e g r a l 2 e^{\frac{- x}{3}}

in t e g r a l \frac{1}{x ^{3} y ^{2}}

in t e g r a l (100 + 2 x)^{- 1}

in t e g r a l x (2 x + 1)^{3}

in t e g r a l x (x + 2)^{\frac{1}{2}}