anti derivative of ax^n is (a/n+1)x^(n+1) a is a const n is power of variable and answere6x^2
-(1/2)X^2 [negative half X squared]
For positive x, this expression is equal to 1. The integral (anti-derivative) is therefore x + C (where C is the arbitrary integration constant). For negative x, this expression is equal to -1, and the integral is -x + C. Wolfram Alpha gives the integral as x times sgn(x), where sgn(x) is the "sign" function.
It is -1 over x-squared.
X^n+1/n+1 X^-2/-2 0r -1/2X^-2
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
X/1 is just X. so (1/2)X2 + C or X2/2 + C
x (ln x + 1) + Constant
Derivative of 1/x 1/x = x-1 Take the derivative (-1)x(-1-1) = -x-2 = 1/x2
anti derivative of ax^n is (a/n+1)x^(n+1) a is a const n is power of variable and answere6x^2
-(1/2)X^2 [negative half X squared]
3
For positive x, this expression is equal to 1. The integral (anti-derivative) is therefore x + C (where C is the arbitrary integration constant). For negative x, this expression is equal to -1, and the integral is -x + C. Wolfram Alpha gives the integral as x times sgn(x), where sgn(x) is the "sign" function.
If f(x)=1/x then F(x)=antiderivative of f(x)=ln(|x|) (the natural log of the absolute value of x) There's another way of reading this question. The anti derivative of 1 is x+c. Dividing that by x gives you 1 + c/x
It is -1 over x-squared.
X^n+1/n+1 X^-2/-2 0r -1/2X^-2
The antiderivative of x2 + x is 1/3x3 + 1/2x2 + C.