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Rewrite the integrand $x\left(\frac{3}{x^4}- 3^{\left(-x+1\right)}+\frac{2}{3x-1}\right)$ in expanded form

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$\int\left(\frac{3}{x^{3}}-x\cdot 3^{\left(-x+1\right)}+\frac{2x}{3x-1}\right)dx$

Learn how to solve problems step by step online. Find the integral int(x(3/(x^4)-3^(-x+1)2/(3x-1)))dx. Rewrite the integrand x\left(\frac{3}{x^4}- 3^{\left(-x+1\right)}+\frac{2}{3x-1}\right) in expanded form. Expand the integral \int\left(\frac{3}{x^{3}}-x\cdot 3^{\left(-x+1\right)}+\frac{2x}{3x-1}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. Take out the constant 2 from the integral. The integral \int\frac{3}{x^{3}}dx results in: \frac{-3}{2x^{2}}.

** Final answer to the problem

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