Please, help me solve
x^2 f(x) = x+ integral_1^x (t f(t))/(t+1) dt, x=1

Question

Please, help me solve
x^2 f(x) = x+ integral_1^x (t f(t))/(t+1) dt, x>=1

stamp · Answer

not sure what that is supposed to be

anonymous · Answer

$$x^2f(x)=x+\int_1^x \frac{t\;f(t)}{t+1}dt,\;x\ge1$$
I don't know either. Solving for f(x)? Finding f '(x)? @cke8, need more details.

experimentx · Answer

differentiate it and get differential equation and solve it.

anonymous · Answer

The only thing I know is that I should solve that integration equation but I don't know how! Do you?

abb0t · Answer

I believe that you're being tested the Fundamental Theorem of Calculus Pt. i

anonymous · Answer

Find $$f(x)$$ that's about he only they can ask here.

anonymous · Answer

Here, first apply the derivative to everything  with respect to x so,

$$ 2xf(x)+2x^2f\prime(x)=1+\frac{xf(x)}{x+1}$$
Next regroup so,
$$ 2x^2f\prime(x)-1=\frac{xf(x)}{x+1}-2xf(x)$$
$$ 2x^2f\prime(x)-1=\left( \frac{x}{x+1}-2x \right) f(x)$$
$$ \frac{ 2x^2f\prime(x)-1}{\left( \frac{x}{x+1}-2x \right) }=f(x)$$
And there you go, if they ask for the derivative jut solve for it.

anonymous · Answer

Thanks a lot!