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

The integral of ((3x-2)^2-(3x+2)^2)/(x^2) is -24ln|x|+C

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

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

- 24 ln ∣ x ∣ + C

Solution steps

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

Simplify

\frac{( 3 x - 2 ) ^{2} - ( 3 x + 2 ) ^{2}}{x ^{2}} : - \frac{24}{x}

= \int - \frac{24}{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 24 \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= - 24 ln ∣ x ∣

Add a constant to the solution

= - 24 ln ∣ x ∣ + C

\frac{d y}{d x} = sin (x) y + e^{x}

y = x^{1 - x}

f (x) = \frac{1}{( 1 + x ^{2} )}

\frac{d}{d x} (4 - \frac{20}{x ^{3}} + \frac{3}{x ^{5}})

f (x) = x^{2} + x, at (x = 1)

What is the integral of ((3x-2)^2-(3x+2)^2)/(x^2) ?
The integral of ((3x-2)^2-(3x+2)^2)/(x^2) is -24ln|x|+C