Solve ∫ 2^-2+(-2)^-2

$$\int 2 ^ { - 2 } + ( - 2 ) ^ { - 2 }$$

Evaluate

$$\frac{x}{2}+С$$

Solution Steps

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\int \frac{1}{4}+\left(-2\right)^{-2}\mathrm{d}x$$

Calculate -2 to the power of -2 and get \frac{1}{4}.

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

Add \frac{1}{4} and \frac{1}{4} to get \frac{1}{2}.

$$\int \frac{1}{2}\mathrm{d}x$$

Find the integral of \frac{1}{2} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{x}{2}$$

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.

$$\frac{x}{2}+С$$

Differentiate w.r.t. x

$$\frac{1}{2} = 0.5$$