Solve ∫ ((y+1)^2/x)

$$\int ( \frac { ( y + 1 ) ^ { 2 } } { x } )$$

Evaluate

$$\left(y+1\right)^{2}\ln(|x|)+С$$

Solution Steps

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

$$\left(y+1\right)^{2}\int \frac{1}{x}\mathrm{d}x$$

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

$$\left(y+1\right)^{2}\ln(|x|)$$

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.

$$\left(y+1\right)^{2}\ln(|x|)+С$$

Differentiate w.r.t. x

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