Trouble solving a separable ODE with constant I have $\frac{dx}{dt} = r(x^n)$ where r is a constant. 
I've tried to solve as a separable ode and have ended up with 
$x^{1-n} = (1-n)(rt+c)$
From here, take logs, solve for $x$ and get 
$x=e + e^{(rt+c)/(1-n)} $  which I'm pretty convinced isn't right. 
However plugging the ODE into wolfram alpha gives the answer 
$x(t) = ((n-1) (c_1-r t))^{1/(1-n)}$ which I equally don't understand. 

Notice, the constant of integration may have positive or negative value.   
using variable separable method as follows  $$\frac{dx}{dt}=rx^n$$
$$\frac{dx}{x^{n}}=rdt$$
$$\int x^{-n}\ dx=r\int dt$$
$$\frac{x^{-n+1}}{-n+1}=rt+c$$
$$x^{1-n}=(1-n)(rt+c)$$
Now, substituting another constant $\color{red}{c=-c_1}$ (as it makes no difference)
$$x^{1-n}=(1-n)(rt-c_1)$$
$$x=\left((1-n)(rt-c_1)\right)^{1/(1-n)}$$
$$x(t)=\left((n-1)(c_1-rt)\right)^{1/(1-n)}$$
