What is the integral of 4x^{-2}+3x^{-1}-1 ?

The integral of 4x^{-2}+3x^{-1}-1 is -4/x+3ln|x|-x+C

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integral of 4x^{-2}+3x^{-1}-1

\int 4 x^{- 2} + 3 x^{- 1} - 1 d x

- \frac{4}{x} + 3 ln ∣ x ∣ - x + C

Solution steps

\int 4 x^{- 2} + 3 x^{- 1} - 1 d x

Simplify

4 x^{- 2} + 3 x^{- 1} - 1 : \frac{4}{x ^{2}} + \frac{3}{x} - 1

= \int \frac{4}{x ^{2}} + \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{4}{x ^{2}} d x + \int \frac{3}{x} d x - \int 1 d x

\int \frac{4}{x ^{2}} d x = - \frac{4}{x}

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int 1 d x = x

= - \frac{4}{x} + 3 ln ∣ x ∣ - x

Add a constant to the solution

= - \frac{4}{x} + 3 ln ∣ x ∣ - x + C

x \to 2 π lim (sin (x))

\int - \frac{1}{2} e^{- 2 v} d v

\frac{d y}{d x} = - \frac{1}{2} y + x

\int \frac{ln ( x )}{2} d x

cos^{2} (3 x)

What is the integral of 4x^{-2}+3x^{-1}-1 ?
The integral of 4x^{-2}+3x^{-1}-1 is -4/x+3ln|x|-x+C