# Find Integration of (x^3)/(x^3) - 2x - 3 ???

Mar 15, 2018

$\int {x}^{3} / {x}^{3} - 2 x - 3 \mathrm{dx} = - {x}^{2} - 2 x + \text{C}$

#### Explanation:

Given: $\int {x}^{3} / {x}^{3} - 2 x - 3 \mathrm{dx}$

We can simplify the integral as:

$\int 1 - 2 x - 3 \mathrm{dx}$

$\int - 2 x - 2 \mathrm{dx}$

Next we integrate each term

$\int - 2 x \mathrm{dx} + \int - 2 \mathrm{dx}$

$\int - 2 x \mathrm{dx} = - \frac{2 {x}^{2}}{2} = - {x}^{2}$

$\int - 2 \mathrm{dx} = - 2 x$

Therefore,

$\int - 2 x \mathrm{dx} + \int - 2 \mathrm{dx} = - {x}^{2} - 2 x + \text{C}$

Mar 23, 2018

$- 2 x - {x}^{2} + C$

#### Explanation:

We are given: $\int \left({x}^{3} / {x}^{3} - 2 x - 3\right) \setminus \mathrm{dx}$

We see that ${x}^{3} / {x}^{3} = 1$, and the integral becomes:

$= \int \left(1 - 2 x - 3\right) \setminus \mathrm{dx}$

Combining like-terms, we get,

$= \int \left(- 2 - 2 x\right) \setminus \mathrm{dx}$

Now, we use the sum rule, and we can split the integral into,

$= \int \left(- 2\right) \setminus \mathrm{dx} + \int \left(- 2 x\right) \setminus \mathrm{dx}$

$= - 2 x + \left(- {x}^{2}\right)$

$= - 2 x - {x}^{2}$

Now, we just need to add a constant, and we get,

$= - 2 x - {x}^{2} + C$