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

The integral of (2x^2+1/((4x)^2)) is (2x^3)/3+1/(16x)-1/(8x)+C

Popular >

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

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

\frac{2 x ^{3}}{3} + \frac{1}{16 x} - \frac{1}{8 x} + C

Solution steps

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

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

\int \frac{1}{( 4 x ) ^{2}} d x = \frac{1}{16 x} - \frac{1}{8 x}

= \frac{2 x ^{3}}{3} + \frac{1}{16 x} - \frac{1}{8 x}

Add a constant to the solution

= \frac{2 x ^{3}}{3} + \frac{1}{16 x} - \frac{1}{8 x} + C

\frac{d}{d y} (\frac{x}{2 y ^{4}})

\frac{\partial}{\partial z} (x cos (y))

x \to 0 + lim ((1 - x)^{(\frac{1}{x})})

2 x y^{^{'}} - 6 y = x^{- 4}

x \to (\frac{π}{2}) - lim (sec (x))

What is the integral of (2x^2+1/((4x)^2)) ?
The integral of (2x^2+1/((4x)^2)) is (2x^3)/3+1/(16x)-1/(8x)+C