Question

find dy/dx

Answer 1

\[\int\limits_{0}^{x} \frac{ 5 }{ 1-t^2 }\] dt

Answer 2

$$\begin{align*}
\frac{5}{1-t^2}=\frac 52\left[\frac{1}{1-t}-\frac{1}{1+t}\right]
\end{align*}$$

Answer 3

That's an interesting equation @BAdhi , where did you get it?

Answer 4

I made a tiny mistake it should be
$$\frac 52\left[\frac{1}{1-t}+\frac{1}{1+t}\right]$$

this is
just partial fractions

Answer 5

Yeah but memorizing that partial fraction is pretty intense man.

Answer 6

with some practice in partial fractions these things just comes to the mind (of course sometimes with small mistakes :) )

Answer 7

What we actually have to find ? Integrand or dy/dx ?

Answer 8

find dy/dx

Answer 9

Then simply differentiate it. No worries then

Answer 10

It makes sense if it is,
$$y=\int \limits_0^x \frac{5}{1-t^2}dt$$

if so the differentiation would be $$\frac{5}{1-x^2}$$ because,
take,
$$y=\int_a^x f(t) dt=F(x)-F(a)$$
with$$\int f(t)dt =F(t)$$
then,$$\frac{dy}{dx}=\frac{d[F(x)-F(a)]}{dx}=\frac{dF(x)}{dx}=f(x) $$