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Popular >

integral of 1-3/x

Solution

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

Solution

x - 3 ln ∣ x ∣ + C

Solution steps

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

\int 1 d x = x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= x - 3 ln ∣ x ∣

Add a constant to the solution

= x - 3 ln ∣ x ∣ + C

Popular Examples

integral of ln(sqrt(x)+sqrt(x+1))

\int ln (x + x + 1) d x

integral of xcos(21x)

\int x cos (21 x) d x

integral of x^2e^{-x^3}sin^2(x^3)

\int x^{2} e^{- x^{3}} sin^{2} (x^{3}) d x

(\partial)/(\partial x)(sin(y-5x))

\frac{\partial}{\partial x} (sin (y - 5 x))

limit as x approaches pi/2 of sqrt(7e^{-2)}

x \to \frac{π}{2} lim (7 e^{- 2})

Frequently Asked Questions (FAQ)

What is the integral of 1-3/x ?
The integral of 1-3/x is x-3ln|x|+C