$$F(x)=f(g(x)), \space f'(x)=\frac{x^2+1}{x-5}, \space g(x)=\sqrt{x}.$$
Find F(x).

Question

$$F(x)=f(g(x)),  \space f'(x)=\frac{x^2+1}{x-5}, \space g(x)=\sqrt{x}.$$
Find F(x).

myininaya · Answer

so we need to find f
so we need to integrate f'
$$\int\limits_{}^{}\frac{x^2+1}{x-5} dx$$

myininaya · Answer

x+5
       ----------
x-5|  x^2+0x+!
      -(x^2-5x)
       -----------
                5x+1
              -(5x-25)
           ----------
                      26

so we have
$$\int\limits_{}^{}(x+5+\frac{26}{x-5}) dx$$

anonymous · Answer

$$F =\rightarrow \sum_{^{_{_{\sqrt[\sqrt[?]{?}]{?}}^{?}}}}^{?}$$

myininaya · Answer

$$f(x)=\frac{x^2}{2}+5x+26 \ln |x-5|+C$$
now we can find f(g(x))

anonymous · Answer

$$F(x)=\frac x2+5\sqrt{x}+26\ln |\sqrt{x}-5|+C$$

anonymous · Answer

looks good on the domain [0,25)u(25,infinity) as expected...

myininaya · Answer

Oh I didn't realize this was Broken Fixer's question. lol

amistre64 · Answer

quick! delete it lol

myininaya · Answer

Broken Fixer knows everything.

anonymous · Answer

$$F(x)`=\frac 12+5\frac{1}{2\sqrt{x}}+\frac{13}{\sqrt{x}(\sqrt{x}-5)}$$