Question

Salut, ma puteti ajuta la problema cu integrala ? Am incercat sa il pun pe t^{2} =y insa nu iasa dupaia...

Answer 1

$\boxed{\int \dfrac{\Big(u(x)\Big)'}{\Big(u(x)\Big)^2-a^2} \, dx = \dfrac{1}{2a}\ln\Big|\dfrac{u(x)-a}{u(x)+a}\Big|+C}\\ \\ \\ \int \dfrac{4t}{t^4-1} \, dt = \int \dfrac{4t}{({t^2)}^2-1} \, dt = \int \dfrac{2\cdot (2t)}{{(t^2)}^2-1} \, dt = 2\cdot \int \dfrac{(t^2)'}{{(t^2)}^2-1^2} \, dt = \\ \\ = 2\cdot \dfrac{1}{2\cdot 1}\ln \Big|\dfrac{t^2-1}{t^2+1}\Big|+C = \ln \Big|\dfrac{t^2-1}{t^2+1}\Big|+C$