I have following equation given.
$$\int_{} \frac{(vdv)^2}{A^2+\sqrt{3}}$$ $$=\frac{v^3}{3 \sqrt{3} A^2}$$
In the first equation I have $(vdv)^2$. There's square on $dv$ also. So, is my integration correct? I found a question similar to this. In that question most of people used multi-variable calculus. So, Does it mean this question doesn't make any sense?
I found a website which is called [Calculus Calculator](https://www.mathway.com/Calculus). I had tried simple equation with that website. I found following result.
Question :
$$\int (xdx)^2$$
Answer : $$\frac{1}{5}d^2x^5+C$$
I got answer but, I would request to explain it
When I tried the problem in this site. I got following result.
$$\frac{d^2(A^2-\sqrt{3})v^5}{5(A^4-3)}+C$$