What is the integral of (x^3-1/(2x)+1) ?

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

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integral of (x^3-1/(2x)+1)

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

\frac{x ^{4}}{4} - \frac{1}{2} ln ∣ x ∣ + x + C

Solution steps

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

\int x^{3} d x = \frac{x ^{4}}{4}

\int \frac{1}{2 x} d x = \frac{1}{2} ln ∣ x ∣

\int 1 d x = x

= \frac{x ^{4}}{4} - \frac{1}{2} ln ∣ x ∣ + x

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{1}{2} ln ∣ x ∣ + x + C

\int - sin (- x) d x

\frac{\partial}{\partial x} (x^{3} + x)

\int_{b}^{1} 3 ln (x) d x

\int 5 x \frac{3}{2} d x

\frac{d}{d x} (\frac{e ^{- x}}{x})

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