Question

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

Answer 1

`intx^3/x^3-2x-3dx=-x^2-2x+"C"`

Explanation:

Given: `intx^3/x^3-2x-3dx`

We can simplify the integral as:

`int1-2x-3dx`

`int-2x-2dx`

Next we integrate each term

`int-2xdx+int-2dx`

`int-2xdx=-(2x^2)/2=-x^2`

`int-2dx=-2x`

Therefore,

`int-2xdx+int-2dx=-x^2-2x+"C"`

Answer 2

`-2x-x^2+C`

Explanation:

We are given: `int(x^3/x^3-2x-3) \ dx`

We see that `x^3/x^3=1`, and the integral becomes:

`=int(1-2x-3) \ dx`

Combining like-terms, we get,

`=int(-2-2x) \ dx`

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

`=int(-2) \ dx+int(-2x) \ dx`

`=-2x+(-x^2)`

`=-2x-x^2`

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

`=-2x-x^2+C`