Solve ∫ ln2x*x wrt x

$$\int \ln 2 x \cdot x d x$$

Evaluate

$$x\ln(x^{2})+\ln(2)x-2x+С$$

Solution Steps

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$\frac{\int \ln(2xx)\mathrm{d}x}{\ln(e)}$$

Simplify.

$$\frac{x\left(\ln(2)+\ln(x^{2})-2\right)}{\ln(e)}$$

Simplify.

$$x\left(\ln(2)+\ln(x^{2})-2\right)$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$x\left(\ln(2)+\ln(x^{2})-2\right)+С$$

Differentiate w.r.t. x

$$\ln(x^{2})+\ln(2)$$