Solve ∫ x+1/x^2+x wrt x

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

Evaluate

$$\ln(|x|)+С$$

Solution Steps

Factor the expressions that are not already factored in \frac{x+1}{x^{2}+x}.

$$\int \frac{x+1}{x\left(x+1\right)}\mathrm{d}x$$

Cancel out x+1 in both numerator and denominator.

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

Use \int \frac{1}{x}\mathrm{d}x=\ln(|x|) from the table of common integrals to obtain the result.

$$\ln(|x|)$$

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.

$$\ln(|x|)+С$$

Differentiate w.r.t. x

$$\frac{1}{x}$$