$$ A _ { 1 } = \int 2 x ( x ^ { 2 } - 5 ) d x $$

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Calculate or simplify the expression $$ \int 2x(x^2-5)dx $$.
Evaluate the integral by following steps:
- step0: Evaluate using formulas and rules:
  $$\int 2x\left(x^{2}-5\right) dx$$
- step1: Multiply the terms:
  $$\int \left(2x^{3}-10x\right) dx$$
- step2: Use properties of integrals:
  $$\int 2x^{3} dx+\int -10x dx$$
- step3: Evaluate the integral:
  $$\frac{x^{4}}{2}+\int -10x dx$$
- step4: Evaluate the integral:
  $$\frac{x^{4}}{2}-5x^{2}$$
- step5: Add the constant of integral C:
  $$\frac{x^{4}}{2}-5x^{2} + C, C \in \mathbb{R}$$
The integral of $$2x(x^2-5)$$ with respect to $$x$$ is $$\frac{x^4}{2}-5x^2 + C$$, where $$C$$ is an arbitrary constant.
The integral of $$2x(x^2-5)$$ with respect to $$x$$ is $$\frac{x^4}{2}-5x^2 + C$$.

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