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
negative cotangent -- dcot(x)/dx=-csc^2(x)
The derivative of cos(x) equals -sin(x); therefore, the anti-derivative of -sin(x) equals cos(x).
X = √63
Assuming you mean x squared plus 5x squared... the answer is 6x squared.
X + y
x squared
Let k = 0 9x18 squared x 17 x 18 k is a constant. Its anti-derivative is kx + C, where C is a constant. The anti-derivative squared is (kx+ C) squared.
∫ (x2+3) = ∫x2 + ∫3(1/3)X3 + 3X + C
-(1/2)X^2 [negative half X squared]
negative cotangent -- dcot(x)/dx=-csc^2(x)
14x
find anti derivative of f(x) 5x^4/3 + 8x^5/4
f(x) = 3x2 + 5x + 2fprime(x) = 6x + 5
The anti-derivative of sqrt(x) : sqrt(x)=x^(1/2) The anti-derivative is x^(1/2+1) /(1/2+1) = (2/3) x^(3/2) The anti-derivative is 4e^x is 4 e^x ( I hope you meant e to the power x) The anti-derivative of -sin(x) is cos(x) Adding, the anti-derivative is (2/3) x^(3/2) + 4 e^x + cos(x) + C
derivative of sec2(x)=2tan(x)sec2(x)
the derivative of 3x is 3 the derivative of x cubed is 3 times x squared
10 x