Solve ∫ du/2^2+1

$$\int \frac { d u } { 2 ^ { 2 } + 1 }$$

Evaluate

$$\frac{u}{5}+С$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\int \frac{1}{4+1}\mathrm{d}u$$

Add 4 and 1 to get 5.

$$\int \frac{1}{5}\mathrm{d}u$$

Find the integral of \frac{1}{5} using the table of common integrals rule \int a\mathrm{d}u=au.

$$\frac{u}{5}$$

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.

$$\frac{u}{5}+С$$

Differentiate w.r.t. u

$$\frac{1}{5} = 0.2$$