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

The integral of (2x^2+1/((2x)^2)) is (2x^3)/3+1/(4x)-1/(2x)+C

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

\int (2 x^{2} + \frac{1}{( 2 x ) ^{2}}) d x

\frac{2 x ^{3}}{3} + \frac{1}{4 x} - \frac{1}{2 x} + C

Solution steps

\int 2 x^{2} + \frac{1}{( 2 x ) ^{2}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x^{2} d x + \int \frac{1}{( 2 x ) ^{2}} d x

\int 2 x^{2} d x = \frac{2 x ^{3}}{3}

\int \frac{1}{( 2 x ) ^{2}} d x = \frac{1}{4 x} - \frac{1}{2 x}

= \frac{2 x ^{3}}{3} + \frac{1}{4 x} - \frac{1}{2 x}

Add a constant to the solution

= \frac{2 x ^{3}}{3} + \frac{1}{4 x} - \frac{1}{2 x} + C

f (x) = - 2 x sin (x^{2})

\frac{\partial}{\partial c} (\frac{a ^{3} b ^{4}}{c ^{2} d ^{4}})

f (x) = arccos (x)

\frac{d}{d x} (3 x e^{- 3 x})

\frac{\partial}{\partial x} (2 cos (4 x))

What is the integral of (2x^2+1/((2x)^2)) ?
The integral of (2x^2+1/((2x)^2)) is (2x^3)/3+1/(4x)-1/(2x)+C