Solve ∫ frac{sqrt{n}}{lnn}

$$\int \frac { \sqrt { n } } { \ln n }$$

Evaluate

$$\frac{\sqrt{n}x}{\ln(n)}+С$$

Solution Steps

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

$$\frac{\sqrt{n}}{\log_{e}\left(n\right)}x$$

Simplify.

$$\frac{\sqrt{n}x}{\ln(n)}$$

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.

$$\frac{\sqrt{n}x}{\ln(n)}+С$$

Differentiate w.r.t. x

$$\frac{\sqrt{n}}{\ln(n)}$$