Question

ermine the
$\int ( 4 x ^ { + } - 3 x ^ { 2 } - 2 ) d x$

Explanation:

Step1: Integrate each term separately

$$\int(4x^+ - 3x^2 - 2)dx=\int4x^+dx-\int3x^2dx-\int2dx$$

Step2: Apply power rule for integration $\int x^n dx=\frac{x^{n + 1}}{n+1}+C(n

eq - 1)$ and $\int kdx=kx + C$ (where $k$ is a constant)
For $\int4x^+dx$, assume it is $\int4x^4dx$ (maybe a writing - error in the original problem). Then $\int4x^4dx=4\times\frac{x^{4 + 1}}{4+1}=\frac{4x^5}{5}$; $\int3x^2dx=3\times\frac{x^{2+1}}{2 + 1}=x^3$; $\int2dx=2x$

Step3: Combine the results

$$\int(4x^4 - 3x^2 - 2)dx=\frac{4x^5}{5}-x^3-2x + C$$

Answer:

$\frac{4x^5}{5}-x^3-2x + C$