The anti derivative of negative sine is cosine.
.0015x2
2.5x2 + any constant
We say function F is an anti derivative, or indefinite integral of f if F' = f. Also, if f has an anti-derivative and is integrable on interval [a, b], then the definite integral of f from a to b is equal to F(b) - F(a) Thirdly, Let F(x) be the definite integral of integrable function f from a to x for all x in [a, b] of f, then F is an anti-derivative of f on [a,b] The definition of indefinite integral as anti-derivative, and the relation of definite integral with anti-derivative, we can conclude that integration and differentiation can be considered as two opposite operations.
x (ln x + 1) + Constant
d/dx (-cscx-sinx)=cscxcotx-cosx
Trig functions have their own special derivatives that you will have to memorize. For instance: the derivative of sinx is cosx. The derivative of cosx is -sinx The derivative of tanx is sec2x The derivative of cscx is -cscxcotx The derivative of secx is secxtanx The derivative of cotx is -csc2x
Using the u substitution method of derivation (selecting sinx as u and cosxdx as du), you get f'(x)=cscx.
The anti derivative of negative sine is cosine.
.0015x2
An integral and an anti-derivative are the same thing. Integration means the process of finding the integral, just as anti-differentiation means the process of finding the anti-derivative.
x squared
find anti derivative of f(x) 5x^4/3 + 8x^5/4
anti derivative of ax^n is (a/n+1)x^(n+1) a is a const n is power of variable and answere6x^2
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
2.5x2 + any constant
According to Wolfram Alpha, input:integral csc x it is -log[cot(x) + csc(x)] + constant You can verify this by taking the derivative of the purported integral.