## iouri.gordon Group Title I wander if my thinking is right when solving this equation. I put details in the post. Don't know how to write an equation in the initial message. So when you click on the message you'll see details. 11 months ago 11 months ago

1. iouri.gordon Group Title

Find $F \prime \left( X \right)$ if $F \left( X \right)=\int\limits_{x}^{x ^{2}}\tan u du$. So what I though is by FTC 1 $F \left( X \right)=F \left( X ^{2} \right)-F \left( X \right)$, now taking derivative of both sides gives: $F \prime \left( X \right) = 2XF \prime \left( X ^{2} \right)-F \prime \left( X \right)$, which in turn could be rewritten as: $2x \frac{ d }{ dx }\int\limits_{0}^{x ^{2}}\tan u du - \frac{ d }{ dx }\int\limits_{0}^{x}\tan udu$ which in turn equals: $2x \tan x ^{2}-\tan x$. Am I doing the right thing?

2. jostiniane Group Title

I dont think my friend ?_? you could take another function G(X) instead taking the same F(X) ... but why not integrating tan(X) like sin/cos => -sin/-cos => -(sin/-cos) => f'/f => -ln|-cos|

3. Anunnaki Group Title

$\int\limits_{x}^{x^2}\tan(u)du \rightarrow \ln \left( \cos(x) \right) - \ln(\cos(x ^{2}))$