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Popular >

integral of (3-x)/x

Solution

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

Solution

3 ln ∣ x ∣ - x + C

Solution steps

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

Expand

\frac{3 - x}{x} : \frac{3}{x} - 1

= \int \frac{3}{x} - 1 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 \frac{3}{x} d x - \int 1 d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int 1 d x = x

= 3 ln ∣ x ∣ - x

Add a constant to the solution

= 3 ln ∣ x ∣ - x + C

Popular Examples

integral of x/(4+25x^2)

\int \frac{x}{4 + 25 x ^{2}} d x

integral of u^{-4}

\int u^{- 4} d u

integral of v/(v+1)

\int \frac{v}{v + 1} d v

integral of x^9\sqrt[3]{x^{10}+4}

integral of 12sin(2x)

\int 12 sin (2 x) d x

Frequently Asked Questions (FAQ)

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