What is the integral of (x^{3/2}-2x^6-1.2)/x ?

The integral of (x^{3/2}-2x^6-1.2)/x is 0.66666…x^{3/2}-0.33333…x^6-1.2ln|x|+C

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integral of (x^{3/2}-2x^6-1.2)/x

\int \frac{x ^{\frac{3}{2}} - 2 x ^{6} - 1.2}{x} d x

0.66666 \dots x^{\frac{3}{2}} - 0.33333 \dots x^{6} - 1.2 ln ∣ x ∣ + C

Solution steps

\int \frac{x ^{\frac{3}{2}} - 2 x ^{6} - 1.2}{x} d x

Expand

\frac{x ^{\frac{3}{2}} - 2 x ^{6} - 1.2}{x} : x^{\frac{1}{2}} - 2 x^{5} - \frac{1.2}{x}

= \int x^{\frac{1}{2}} - 2 x^{5} - \frac{1.2}{x} 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^{\frac{1}{2}} d x - \int 2 x^{5} d x - \int \frac{1.2}{x} d x

\int x^{\frac{1}{2}} d x = \frac{2}{3} x^{\frac{3}{2}}

\int 2 x^{5} d x = \frac{x ^{6}}{3}

\int \frac{1.2}{x} d x = 1.2 ln ∣ x ∣

= \frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{6}}{3} - 1.2 ln ∣ x ∣

Simplify

= 0.66666 \dots x^{\frac{3}{2}} - 0.33333 \dots x^{6} - 1.2 ln ∣ x ∣

Add a constant to the solution

= 0.66666 \dots x^{\frac{3}{2}} - 0.33333 \dots x^{6} - 1.2 ln ∣ x ∣ + C

\int \frac{x ^{2} - x + 2}{x ^{3} + x} d x

x \to 0 - lim (\frac{14 x ^{4} - 14 x}{x})

\frac{\partial}{\partial x} (x^{3} y + sin (x y))

\frac{d}{d x} (3 x^{2} - 4 x - 5)

\frac{( - s - 1 )}{s ^{2} + s + 1}

What is the integral of (x^{3/2}-2x^6-1.2)/x ?
The integral of (x^{3/2}-2x^6-1.2)/x is 0.66666…x^{3/2}-0.33333…x^6-1.2ln|x|+C