Solve ∫ ln^nx wrt x

$$\int \ln ^ { n } x d x$$

Evaluate

$$nx\left(\ln(x)-1\right)+С$$

Solution Steps

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

$$\frac{\int \ln(x^{n})\mathrm{d}x}{\ln(e)}$$

Simplify.

$$\frac{n\ln(x)x-nx}{\ln(e)}$$

Simplify.

$$n\ln(x)x-nx$$

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.

$$n\ln(x)x-nx+С$$

Differentiate w.r.t. x

$$n\ln(x)$$