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Antiderivative
An antiderivative of a function f(x) is just a function whose derivative is f(x).  
Example
Since the derivative of x^{2}+4 is 2x, an antiderivative of 2x is x^{2}+4.
Every antiderivative of 2x has the form x^{2} + C, where C is constant 

Notation
We write
Here is how we read the formula:

Fill in the blanks and press "Check." (Write x^{3} as x^3, andx^{2} as x^2, and don't forget to include the "dx" and the "+C" in the proper places. Include as many spaces as you want; they will be ignored.)
Since the derivative of x^3 is 3x^2,
Now do one yourself:
Now, a multiple choice question:
The correct answer to the last question suggests a formula for finding the antiderivative of any power of x. The following table includes this formula, as well as other information.
Function  Antiderivative  Formula  
x^{n} (n 1) 





Function  Antiderivative  Formula  
x^{1}  ln x + C 




Function  Antiderivative  Formula  
k (k constant) 
kx + C 




Function  Antiderivative  Formula  
e^{x}  e^{x} + C 



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(  4x  2  +  3x^{1.1} 6)  dx  = ? 








Question
How do we deal with powers of x in the denominator, such as in, say,  5x^{4}  ? 
Answer
First convert them into exponent form; that is, rewrite the expression with all powers of x in the numerator. For example, rewrite
5x^{4}  as  5  x^{4.} 
In exponent form, the expression  6x  +  6  4x^{1}  is ? 
Fill in the blank and press "Check." Use standard calculator formatting; for example, write
4  as either  5x^2/4,  (5x^2)/4,  or  (5/4)x^2,  but not  5/4x^2. 
and write ln x just like it is written here. Spaces will be ignored.
(Do not use "*" at all; for example 5e^{x} should be written as 5e^x, and not 5*e^x.)
You now have several options