Solve ∫ x^2/1+x^2 wrt x9

$$\int{ \frac{ { x }^{ 2 } }{ 1+ { x }^{ 2 } } }d x 9$$

Evaluate

$$\frac{x_{9}x^{2}}{x^{2}+1}+С$$

Solution Steps

Find the integral of \frac{x^{2}}{1+x^{2}} using the table of common integrals rule \int a\mathrm{d}x_{9}=ax_{9}.

$$\frac{x^{2}}{1+x^{2}}x_{9}$$

Simplify.

$$\frac{x^{2}x_{9}}{1+x^{2}}$$

If F\left(x_{9}\right) is an antiderivative of f\left(x_{9}\right), then the set of all antiderivatives of f\left(x_{9}\right) is given by F\left(x_{9}\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\frac{x^{2}x_{9}}{1+x^{2}}+С$$

Differentiate w.r.t. x

$$\frac{2xx_{9}}{\left(x^{2}+1\right)^{2}}$$