Question

Stie cineva cum pot rezolva integrala de la 0 la 1 din x+1/x+3 dx.

Answer 1

Explicație pas cu pas:

$\int_{0}^{1} \frac{x + 1}{x + 3} dx = \int_{0}^{1} \left(1 - \frac{2}{x + 3} \right) dx = \int_{0}^{1} 1 dx - 2\int_{0}^{1} \frac{1}{x + 3} dx \\ = x|_{0}^{1} - 2(ln|x + 3|)|_{0}^{1} = 1 - 0 - 2(ln(4) - ln(3)) = 1 - 2 ln( \frac{4}{3} )$