Solve ∫ du/sqrt{u}

$$\int \frac { d u } { \sqrt { u } }$$

Evaluate

$$2\sqrt{u}+С$$

Solution Steps

Rewrite \frac{1}{\sqrt{u}} as u^{-\frac{1}{2}}. Since \int u^{k}\mathrm{d}u=\frac{u^{k+1}}{k+1} for k\neq -1, replace \int u^{-\frac{1}{2}}\mathrm{d}u with \frac{u^{\frac{1}{2}}}{\frac{1}{2}}. Simplify and convert from exponential to radical form.

$$2\sqrt{u}$$

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

$$2\sqrt{u}+С$$

Differentiate w.r.t. u

$$\frac{1}{\sqrt{u}}$$