Question

Problema politehnica

Salut, aveti vreo idee la problema numarul 947 ? Am incercat prin parti insa nu-mi iasa deloc...

Answer 1

$I \int\limits^3_1 \frac{lnx}{ln(x*(4-x))} \, dx$
$x-\ \textgreater \ 4-x=\ \textgreater \ dx=-dx$
$I= \int\limits^1_3 \frac{ln(4-x)}{ln(x*(4-x))} \,- dx = \int\limits^3_1 \frac{ln(4-x)}{ln(x*(4-x))} \, dx$
$2I=I+I= \int\limits^3_1 \frac{lnx}{ln(x*(4-x))} \, dx + \int\limits^3_1 \frac{ln(4-x)}{ln(x*(4-x))} \, dx$
$2I= \int\limits^3_1 \frac{lnx+ln(4-x)}{ln(x*(4-x))} \, dx = \int\limits^3_1 \frac{ln(x*(4-x))}{ln(x*(4-x))} \, dx = \int\limits^3_1 {1} \, dx =3-1=2$
$2I=2=\ \textgreater \ I=1$