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It is not clear whether you are interested in
sqrt(1 - x2) or sqrt(1 + x2)
-1/(2*x2)
The derivative, with respect to x, is -x/sqrt(1-x2)
0
The anti-derivative of X2 plus X is the same as the anti-derivative of X2 plus the anti-derivative of X. The anti derivative of X2 is X3/3 plus an integration constant C1 The anti derivative of X is X2/2 plus an integration constant C2 So the anti-derivative of X2+X is (X3/3)+(X2/2)+C1+C2 The constants can be combined and the fraction can combined by using a common denominator leaving (2X3/6)+(3X2/6)+C X2/6 can be factored out leaving (X2/6)(2X+3)+C Hope that helps
-1
-1
square root of (x2 + 1) = no simplification (square root of x2) + 1 = x + 1
3
The antiderivative of x2 + x is 1/3x3 + 1/2x2 + C.
x2 square root of x is an expression, not an equation or inequality. It, therefore, has no answer.
d/dx (x2+ 9)1/2= 1/2*(x2+ 9)-1/22x = x(x2+ 9)-1/2or x/(x2+ 9)1/2
∫ (x2+3) = ∫x2 + ∫3(1/3)X3 + 3X + C