What is the integral of 5x^{-3}+4x^{-2}-3x^{-1}+4 ?

The integral of 5x^{-3}+4x^{-2}-3x^{-1}+4 is -5/(2x^2)-4/x-3ln|x|+4x+C

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integral of 5x^{-3}+4x^{-2}-3x^{-1}+4

\int 5 x^{- 3} + 4 x^{- 2} - 3 x^{- 1} + 4 d x

- \frac{5}{2 x ^{2}} - \frac{4}{x} - 3 ln ∣ x ∣ + 4 x + C

Solution steps

\int 5 x^{- 3} + 4 x^{- 2} - 3 x^{- 1} + 4 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 5 x^{- 3} d x + \int 4 x^{- 2} d x - \int 3 x^{- 1} d x + \int 4 d x

\int 5 x^{- 3} d x = - \frac{5}{2 x ^{2}}

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

\int 3 x^{- 1} d x = 3 ln ∣ x ∣

\int 4 d x = 4 x

= - \frac{5}{2 x ^{2}} - \frac{4}{x} - 3 ln ∣ x ∣ + 4 x

Add a constant to the solution

= - \frac{5}{2 x ^{2}} - \frac{4}{x} - 3 ln ∣ x ∣ + 4 x + C

\int_{0}^{1} 1 + \frac{9 x}{4} d x

cos (t) y^{^{'}} + sin (t) y = 2 cos^{3} (t) sin (t) - 1

\frac{c}{x}

6 x^{2} ln (6 x)

2^{(x^{2} - 3 x + 8)}

What is the integral of 5x^{-3}+4x^{-2}-3x^{-1}+4 ?
The integral of 5x^{-3}+4x^{-2}-3x^{-1}+4 is -5/(2x^2)-4/x-3ln|x|+4x+C