Solve ∫ wrt y/2sqrt{sqrt{x+1}}

$$\int \frac { d y } { 2 \sqrt { \sqrt { x + 1 } } }$$

Evaluate

$$\frac{y}{2\sqrt[4]{x+1}}+С$$

Solution Steps

Find the integral of \frac{1}{2\sqrt[4]{x+1}} using the table of common integrals rule \int a\mathrm{d}y=ay.

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

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

$$\frac{y}{2\sqrt[4]{x+1}}+С$$

Differentiate w.r.t. x

$$-\frac{y}{8\left(x+1\right)^{\frac{5}{4}}}$$