Answer:
[tex]-\frac{1}{2x^2} - \frac{3}{2}x^2 -4x +c[/tex] Assuming you need the integral this would be the answer.
Step-by-step explanation:
[tex]\int\limits \frac{1}{x^3} -3x \, -4dx[/tex]
Thats after removing parenthesis.
Now we have to split into multiple intergrals..
[tex]\int\ \frac{1}{x^3} \, dx + \int\ -3xdx + \int\-4dx[/tex]
Now we want to move x^3 out of the denom by raising it to the -1 power
[tex]\int\ (x^3)^{-1}dx + \int\- -3xdx+\int\ -4dx[/tex]
Multiply the exponents in (x^3)^-1
We also need to apply the power rule of (a^m)^n = a^mn
[tex]\int\ x^{3*-1}dx+\int\ -3xdx + \int\ -4dx[/tex]
3 by -1
[tex]\int\ x^{-3}dx+\int\ -3xdx + \int\ -4dx[/tex]
Now we want to use the power rule (I assume you know this rule so I won't be posting it) as I with the integral of x^-3 where x is -1/2x^-2
[tex]-\frac{1}{2}x^{-2} + C \int\ -3xdx + \int\ - 4dx[/tex]
Now since -3 is a constant we can move -3 out of the integral since it respects x.
[tex]-\frac{1}{2}x^{-2} + C - 3 \int\ xdx + \int\ -4dx[/tex]
Now we need to remember the power rule with the respect to 1/2x^2 which is respective to x.
[tex]-\frac{1}{2}x^{-2} + C - 3 (\frac{1}{2}x^2 +C)+\int -4dx[/tex]
Then we apply the constat rule (You should know this as well)
[tex]-\frac{1}{2}x^{-2} + C - 3 (\frac{1}{2}x^2+C)-4x+C[/tex]
Now we simplify....
[tex]-\frac{1}{2}x^{-2} + C - 3 (\frac{x^2}{2}+C)-4x + C > -\frac{1}{2x^2} - \frac{3x^2}{2} -4x + C[/tex]
As you can see you just then re-order as above.
