Question

Integral of 2x sqrt(1-x^2)

Answer 1

let u = 1-x^2
so du = -2xdx substitute it into the formula and you get integral of -(u)^1/2du

after everythign is done youre left with u^3/2 / (3/2) +c after u take everything out u'll get -2/3 * (1-x^2)^3/2 + c

Answer 2

\[\int\limits2x \sqrt{1-x^2}dx\]
\[2\int\limits x \sqrt{1-x^2}dx\]
u = 1-x^2
du = -2x dx
\[-\int\limits \sqrt{u}du\]
\[=\frac{2u^{\frac{3}{2}}}{3}+C\]
\[= -\frac{2}{3}(1-x^2)^{\frac{3}{2}}\]