Solve ∫ log(e) wrt x

$$\int{ \log ( e ) }d x$$

Evaluate

$$\log(e)x+С$$

Solution Steps

Find the integral of \log_{10}\left(e\right) using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\log_{10}\left(e\right)x$$

Simplify.

$$\frac{x}{\ln(10)}$$

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.

$$\frac{x}{\ln(10)}+С$$

Differentiate w.r.t. x

$$\log(e)$$