What is the integral of 4x^2+1/((2x)^2) ?

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

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integral of 4x^2+1/((2x)^2)

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

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

Solution steps

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

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

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

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

Add a constant to the solution

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

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