Solve ∫ 2v-1/v^2-v+1

$$\int \frac { 2 v - 1 } { v ^ { 2 } - v + 1 }$$

Evaluate

$$\frac{2vx-x}{v^{2}-v+1}+С$$

Solution Steps

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

$$\frac{2v-1}{v^{2}-v+1}x$$

Simplify.

$$\frac{\left(2v-1\right)x}{v^{2}-v+1}$$

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.

$$\frac{\left(2v-1\right)x}{v^{2}-v+1}+С$$

Differentiate w.r.t. x

$$\frac{2v-1}{v^{2}-v+1}$$