Solve ∫ sqrt{1+4y/4y}

$$\int \sqrt { \frac { 1 + 4 y } { 4 y } }$$

Evaluate

$$\frac{\sqrt{4+\frac{1}{y}}x}{2}+С$$

Solution Steps

Find the integral of \sqrt{\frac{1+4y}{4y}} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\sqrt{\frac{1+4y}{4y}}x$$

Simplify.

$$\frac{\sqrt{\frac{1+4y}{y}}x}{2}$$

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.

$$\frac{\sqrt{\frac{1+4y}{y}}x}{2}+С$$

Differentiate w.r.t. x

$$\frac{\sqrt{4+\frac{1}{y}}}{2}$$