The indefinite integral of $$2x^3-10x+3$$ is:

To start solving for the indefinite integral$\int 2x^3-10x+3 dx$ we may simplify the problem by applying the rule that an integral of a sum is equivalent to the sum of the integrals.

The indefinite integral then becomes $2\int x^3 dx - 10\int x dx + 3\int dx$ and we can start solving for the parts as follows:

$2\int x^3 dx= 2 *\frac{x^{3+1}}{3+1}+C_1= \frac{2}{4}{x}^4 +C_1 = \frac{1}{2}{x}^4 +C_1$

$10\int x dx = 10 *\frac{x^{1+1}}{1+1}+C_2=\frac{10}{2}{x}^2 +C_2= 5x^2 +C_2$

$3\int dx = 3x +C_3$

Let $C = C_1+C_2+C_3$, then let's combine the parts to achieve our overall answer of 

$\int 2x^3-10x+3 dx = \frac{1}{2}{x}^4 - 5x^2 + 3x + C$