Question

Integrala de la 0 la 1 din 3x/(2x+3) dx

Answer 1

Răspuns:

Explicație pas cu pas:

$\displaystyle\int_0^1\dfrac{3x}{2x+3}dx=\dfrac{3}{2}\int_0^1\dfrac{2x+3-3}{2x+3}dx=\dfrac{3}{2}\int_0^1dx-\dfrac{3}{2}\int_0^1 \dfrac{3}{2x+3}dx=\\\dfrac{3}{2}x|_0^1-\dfrac{9}{4}\ln(2x+3)|_0^1=\dfrac{3}{2}-\dfrac{9}{4}\ln\dfrac{5}{3}$