Solve ∫ z/(z-1)^2(z+2)

$$\int \frac { z } { ( z - 1 ) ^ { 2 } ( z + 2 ) }$$

Evaluate

$$\frac{xz}{\left(z+2\right)\left(z-1\right)^{2}}+С$$

Solution Steps

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

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

Simplify.

$$\frac{zx}{\left(z-1\right)^{2}\left(z+2\right)}$$

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.

$$\frac{zx}{\left(z-1\right)^{2}\left(z+2\right)}+С$$

Differentiate w.r.t. x

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