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Popular >

integral of (2x-3)/x

Solution

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

Solution

2 x - 3 ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

\int 2 d x = 2 x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= 2 x - 3 ln ∣ x ∣

Add a constant to the solution

= 2 x - 3 ln ∣ x ∣ + C

Popular Examples

sqrt(x)+sqrt(y)(dy)/(dx)=0,y(16)=4

x + y \frac{d y}{d x} = 0, y (16) = 4

area x= 1/(y^2),x=1,x=4 area

x = \frac{1}{y ^{2}}, x = 1, x = 4

integral of (-8)/(sqrt(x^2+16))

\int \frac{- 8}{x ^{2} + 16} d x

derivative of arctan(sin(7x))

\frac{d}{d x} (arctan (sin (7 x)))

(dy)/(dx)+6y=xe^{-6x}

\frac{d y}{d x} + 6 y = x e^{- 6 x}

Frequently Asked Questions (FAQ)

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