What is the integral of (2x^4x+3x^3-x^2)/(x^3) ?

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

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integral of (2x^4x+3x^3-x^2)/(x^3)

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

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

Solution steps

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

Expand

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

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

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

\int 3 d x = 3 x

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{2 x ^{3}}{3} + 3 x - ln ∣ x ∣

Add a constant to the solution

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

t \to 0 lim (\frac{sin ( t )}{t})

(7 x^{4} - x + 6) (- x^{5} + 1)

\frac{\partial}{\partial u} (2 v)

\int e^{- 3 l n (x)} d x

\int \frac{ln ( x ^{2} )}{x ^{3}} d x

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