Question

AYUDA EN SERIO ES URGENTE ES CALCULO INTEGRAR INVERSA

Answer 1

Cambio de variable

$u=\arccos (2x)\to x =\dfrac{1}{2}\cos u \to dx = -\dfrac{1}{2}\sin u ~du\\\displaystyle\\I=\int u\cdot \left( -\dfrac{1}{2}\sin u\right) ~du\\\\I=\dfrac{1}{2}\int u~d(\cos u)\\\\I=\dfrac{1}{2}\left(u\cos u-\int \cos u ~du\right)\\\\I=\dfrac{1}{2}u\cos u-\dfrac{1}{2}\sin u+C\\\\\text{Restituyendo}\\\\\boxed{I=x\arccos(2x)-\dfrac{\sqrt{1-4x^2}}{2}+C}$