What is the integral of (5x^2+1/((5x)^2)) ?

The integral of (5x^2+1/((5x)^2)) is (5x^3)/3-1/(25x)+C

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integral of (5x^2+1/((5x)^2))

\int (5 x^{2} + \frac{1}{( 5 x ) ^{2}}) d x

\frac{5 x ^{3}}{3} - \frac{1}{25 x} + C

Solution steps

\int 5 x^{2} + \frac{1}{( 5 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 5 x^{2} d x + \int \frac{1}{( 5 x ) ^{2}} d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int \frac{1}{( 5 x ) ^{2}} d x = - \frac{1}{25 x}

= \frac{5 x ^{3}}{3} - \frac{1}{25 x}

Add a constant to the solution

= \frac{5 x ^{3}}{3} - \frac{1}{25 x} + C

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What is the integral of (5x^2+1/((5x)^2)) ?
The integral of (5x^2+1/((5x)^2)) is (5x^3)/3-1/(25x)+C