What is the integral of (24x^6-24x^4+x)/x ?

The integral of (24x^6-24x^4+x)/x is 4x^6-6x^4+x+C

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integral of (24x^6-24x^4+x)/x

\int \frac{24 x ^{6} - 24 x ^{4} + x}{x} d x

4 x^{6} - 6 x^{4} + x + C

Solution steps

\int \frac{24 x ^{6} - 24 x ^{4} + x}{x} d x

Expand

\frac{24 x ^{6} - 24 x ^{4} + x}{x} : \frac{24 x ^{6}}{x} - \frac{24 x ^{4}}{x} + \frac{x}{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 \frac{24 x ^{6}}{x} d x - \int \frac{24 x ^{4}}{x} d x + \int \frac{x}{x} d x

\int \frac{24 x ^{6}}{x} d x = 4 x^{6}

\int \frac{24 x ^{4}}{x} d x = 6 x^{4}

\int \frac{x}{x} d x = x

= 4 x^{6} - 6 x^{4} + x

Add a constant to the solution

= 4 x^{6} - 6 x^{4} + x + C

\int_{- y}^{y} ∣ x ∣ d x

x d y = d x

\frac{\partial}{\partial x} (\frac{6 x}{9 + x ^{2} + y ^{2}})

\frac{d}{d x} (ln (\frac{1 + x}{1 - x}))

\frac{d}{d x} (sin (3 x y))

What is the integral of (24x^6-24x^4+x)/x ?
The integral of (24x^6-24x^4+x)/x is 4x^6-6x^4+x+C