Solve ∫ 1/x^2+x^2

$$\int \frac { 1 } { x ^ { 2 } + x ^ { 2 } }$$

Evaluate

$$-\frac{1}{2x}+С$$

Solution Steps

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

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

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int \frac{1}{x^{2}}\mathrm{d}x with -\frac{1}{x}.

$$-\frac{\frac{1}{x}}{1+1}$$

Simplify.

$$-\frac{1}{2x}$$

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.

$$-\frac{1}{2x}+С$$

Differentiate w.r.t. x

$$\frac{1}{2x^{2}}$$