(d) $$ \int x\left(6 x^{2}-5\right) \mathrm{d} x $$

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Calculate the integral $$ \int x(6x^2-5) \,dx $$.
Evaluate the integral by following steps:
- step0: Evaluate using formulas and rules:
  $$\int x\left(6x^{2}-5\right) dx$$
- step1: Multiply the terms:
  $$\int \left(6x^{3}-5x\right) dx$$
- step2: Use properties of integrals:
  $$\int 6x^{3} dx+\int -5x dx$$
- step3: Evaluate the integral:
  $$\frac{3x^{4}}{2}+\int -5x dx$$
- step4: Evaluate the integral:
  $$\frac{3x^{4}}{2}-\frac{5x^{2}}{2}$$
- step5: Add the constant of integral C:
  $$\frac{3x^{4}}{2}-\frac{5x^{2}}{2} + C, C \in \mathbb{R}$$
The integral of $$x(6x^2-5)$$ with respect to $$x$$ is $$\frac{3x^{4}}{2}-\frac{5x^{2}}{2} + C$$, where $$C$$ is an arbitrary constant.
The integral of $$ x(6x^2 - 5) $$ with respect to $$ x $$ is $$ \frac{3x^{4}}{2} - \frac{5x^{2}}{2} + C $$, where $$ C $$ is a constant.

(d)

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