What is the integral of x^2+1/((3x)^2) ?

The integral of x^2+1/((3x)^2) is (x^3)/3-1/(9x)+C

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integral of x^2+1/((3x)^2)

\int x^{2} + \frac{1}{( 3 x ) ^{2}} d x

\frac{x ^{3}}{3} - \frac{1}{9 x} + C

Solution steps

\int x^{2} + \frac{1}{( 3 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 x^{2} d x + \int \frac{1}{( 3 x ) ^{2}} d x

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

\int \frac{1}{( 3 x ) ^{2}} d x = - \frac{1}{9 x}

= \frac{x ^{3}}{3} - \frac{1}{9 x}

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{1}{9 x} + C

\frac{d}{d x} (2 x^{3} - 15 x^{2} + 36 x + 5)

x^{2} - x, 3 x + 5

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

2 x^{3} y^{^{'}} = y (y^{2} + 3 x^{2})

\int 6 x + 1 d x

What is the integral of x^2+1/((3x)^2) ?
The integral of x^2+1/((3x)^2) is (x^3)/3-1/(9x)+C