Question

Să se calculeze :

$\int6x {(3 {x}^{2} + 1)}^{7} \: dx , \: x\:\in\:\mathbb{R}$

Answer 1

1. Facem #schimbarea_de_variabila 3x^2+1=t ⇒ 6x dx= dt
2. Prin urmare integrala va deveni ∫ t⁷ dt = t⁸/8+C , iar inlocuind obtinem
3. (3x²+1)⁸/8+C
4. Hope you understood!

Answer 2

fie 3x²+1=u

atunci 6xdx=du

∫6x*(3x²+1)^7dx= ∫(3x²+1)^7*6xdx=∫u^7du=u^/8=(1/8)*(3x²+1)^7 +C

as prima schimbarede variabila as that!