(2) $$ \int \frac{10}{\sqrt[3]{3-5 x}} \mathrm{~d} x $$;

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Calculate the integral $$ \int \frac{10}{\sqrt[3]{3-5x}} dx $$.
Evaluate the integral by following steps:
- step0: Evaluate using substitution:
  $$\int \frac{10}{\sqrt[3]{3-5x}} dx$$
- step1: Evaluate the power:
  $$\int \frac{10}{\left(3-5xight)^{\frac{1}{3}}} dx$$
- step2: Rewrite the expression:
  $$\int 10	imes \frac{1}{\left(3-5xight)^{\frac{1}{3}}} dx$$
- step3: Use properties of integrals:
  $$10	imes \int \frac{1}{\left(3-5xight)^{\frac{1}{3}}} dx$$
- step4: Use the substitution $$dx=-\frac{1}{5} dt$$ to transform the integral$$:$$
  $$10	imes \int \frac{1}{\left(3-5xight)^{\frac{1}{3}}}	imes \left(-\frac{1}{5}ight) dt$$
- step5: Simplify:
  $$10	imes \int -\frac{1}{5\left(3-5xight)^{\frac{1}{3}}} dt$$
- step6: Use the substitution $$t=3-5x$$ to transform the integral$$:$$
  $$10	imes \int \frac{-1}{5t^{\frac{1}{3}}} dt$$
- step7: Rewrite the fraction:
  $$10	imes \int -\frac{1}{5t^{\frac{1}{3}}} dt$$
- step8: Rewrite the expression:
  $$10	imes \int -\frac{1}{5}	imes \frac{1}{t^{\frac{1}{3}}} dt$$
- step9: Use properties of integrals:
  $$10\left(-\frac{1}{5}ight)	imes \int \frac{1}{t^{\frac{1}{3}}} dt$$
- step10: Multiply the numbers:
  $$-2	imes \int \frac{1}{t^{\frac{1}{3}}} dt$$
- step11: Evaluate the integral:
  $$-2	imes \frac{t^{-\frac{1}{3}+1}}{-\frac{1}{3}+1}$$
- step12: Simplify:
  $$-2	imes \frac{3}{2}t^{\frac{2}{3}}$$
- step13: Multiply the numbers:
  $$-3t^{\frac{2}{3}}$$
- step14: Substitute back:
  $$-3\left(3-5xight)^{\frac{2}{3}}$$
- step15: Simplify:
  $$-3\sqrt[3]{\left(3-5xight)^{2}}$$
- step16: Add the constant of integral C:
  $$-3\sqrt[3]{\left(3-5xight)^{2}} + C, C \in \mathbb{R}$$
The integral of $$ \frac{10}{\sqrt[3]{3-5x}} $$ with respect to $$ x $$ is $$ -3\sqrt[3]{(3-5x)^{2}} + C $$, where $$ C $$ is an arbitrary constant.
The integral of $$ \frac{10}{\sqrt[3]{3-5x}} $$ with respect to $$ x $$ is $$ -3\sqrt[3]{(3-5x)^{2}} + C $$.

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