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

The integral of 1/2 x^3+2-(x+1) is (x^4)/8-(x^2)/2+x+C

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

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

\frac{x ^{4}}{8} - \frac{x ^{2}}{2} + x + C

Solution steps

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

\int \frac{1}{2} x^{3} d x = \frac{x ^{4}}{8}

\int 2 d x = 2 x

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

= \frac{x ^{4}}{8} + 2 x - (\frac{x ^{2}}{2} + x)

Simplify

= \frac{x ^{4}}{8} - \frac{x ^{2}}{2} + x

Add a constant to the solution

= \frac{x ^{4}}{8} - \frac{x ^{2}}{2} + x + C

\frac{\partial}{\partial x} (2 x^{2} - 3 y - 4)

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

(9 x^{2} - 15 x) e^{x}

4 e^{x^{2}}

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

What is the integral of 1/2 x^3+2-(x+1) ?
The integral of 1/2 x^3+2-(x+1) is (x^4)/8-(x^2)/2+x+C