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

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: \(\int \frac{10}{\left(3-5x\right)^{\frac{1}{3}}} dx\) - step2: Rewrite the expression: \(\int 10\times \frac{1}{\left(3-5x\right)^{\frac{1}{3}}} dx\) - step3: Use properties of integrals: \(10\times \int \frac{1}{\left(3-5x\right)^{\frac{1}{3}}} dx\) - step4: Use the substitution \(dx=-\frac{1}{5} dt\) to transform the integral\(:\) \(10\times \int \frac{1}{\left(3-5x\right)^{\frac{1}{3}}}\times \left(-\frac{1}{5}\right) dt\) - step5: Simplify: \(10\times \int -\frac{1}{5\left(3-5x\right)^{\frac{1}{3}}} dt\) - step6: Use the substitution \(t=3-5x\) to transform the integral\(:\) \(10\times \int \frac{-1}{5t^{\frac{1}{3}}} dt\) - step7: Rewrite the fraction: \(10\times \int -\frac{1}{5t^{\frac{1}{3}}} dt\) - step8: Rewrite the expression: \(10\times \int -\frac{1}{5}\times \frac{1}{t^{\frac{1}{3}}} dt\) - step9: Use properties of integrals: \(10\left(-\frac{1}{5}\right)\times \int \frac{1}{t^{\frac{1}{3}}} dt\) - step10: Multiply the numbers: \(-2\times \int \frac{1}{t^{\frac{1}{3}}} dt\) - step11: Evaluate the integral: \(-2\times \frac{t^{-\frac{1}{3}+1}}{-\frac{1}{3}+1}\) - step12: Simplify: \(-2\times \frac{3}{2}t^{\frac{2}{3}}\) - step13: Multiply the numbers: \(-3t^{\frac{2}{3}}\) - step14: Substitute back: \(-3\left(3-5x\right)^{\frac{2}{3}}\) - step15: Simplify: \(-3\sqrt[3]{\left(3-5x\right)^{2}}\) - step16: Add the constant of integral C: \(-3\sqrt[3]{\left(3-5x\right)^{2}} + C, C \in \mathbb{R}\) 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.