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

Find the integral int(x(1/(3+x^2)-*2^(x-1)3e^(2x)))dx