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Popular >

integral of (3x-2)/x

Solution

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

Solution

3 x - 2 ln ∣ x ∣ + C

Solution steps

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

Expand

\frac{3 x - 2}{x} : 3 - \frac{2}{x}

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

\int 3 d x = 3 x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= 3 x - 2 ln ∣ x ∣

Add a constant to the solution

= 3 x - 2 ln ∣ x ∣ + C

Popular Examples

integral of (8x^5-3x^3-4x^2+6x+3)

\int (8 x^{5} - 3 x^{3} - 4 x^{2} + 6 x + 3) d x

integral of 3/(x*ln^2(3x))

\int \frac{3}{x \cdot ln ^{2} ( 3 x )} d x

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\int (x^{2} + x)^{6} (2 x + 1) d x

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\int x^{2} 7^{x^{3} + 5} d x

integral of (3x-1)(6x^2-4x+1)^{1/3}

\int (3 x - 1) (6 x^{2} - 4 x + 1)^{\frac{1}{3}} d x

Frequently Asked Questions (FAQ)

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