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Powers, Substitutions, Constant of Integration, Absolute Value

Integration


Indefinite Integrals


Powers:


Integration of a linear factor
Integration of a fractional power Integration of a fractional power
Integral of a positive fractional power
Integration of a negative fractional power  
Integral of a negative fractional power
Integral of radical of a power of x Integral of a radical of a power
Integration of the reciprocal of a power Integral of the reciprocal of a power
Integral of the sum of reciprocals
Integration of a factored quadratic Integral of a quadratic
Integral of a polynomial with positive powers Integral of positive powers
 
Integral of a polynomial with negative powers  Integral of negative powers
Integral of a quadratic times a radical
Integral of a quadratic over a radical

 

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Substitution:


 Integral of u*du  
 
Integration of : constant needed  
Integral of unu'dx with a factor x missing
Integral of a root of a quantity, with u' present
Integration of un*du: Linear to a fractional power, constant needed
Integration of un*du: Reciprocal of a radical of a linear, constant needed
Integration of un*du: Reciprocal of (radical times a radical to a power), constant needed

Integration of un*du: Polynomial to a power, constant needed
Integration of un*du: Reciprocal of a radical, constant needed

 

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Determination of the constant of integration:


Integration of un*du and determination of the constant
Integration of f '' and f ' and determination of the constants
 
 

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Definite integrals:


Positive area under a linear function via geometry and definite integral:
Negative area and a linear function via geometry and definite integral:
Negative and positive area and a linear function and the x axis via geometry and definite integral:
Positive area and a quadratic function via geometry and definite integral:
Negative area and a quadratic function via geometry and definite integral:
Negative and positive area and a quadratic function via geometry and definite integral:

 Integration of an odd power, various limits Definite integral of an odd power
Integration of an even power, various limits Definite integral of an even  power
Definite Integral of an Odd Fractional Power, various limits
Definite Integral of Mixed Powers, symmetric limits
Definite Integral of a Quadratic over a Fractional Power
Definite Integral of the reciprocal of a radical times a power
 Definite integral of a linear factor in quadrants 4 and 1  
Definite integral of a quadratic, quadrants 4 and 1
 
Definite integral of a negative power in quadrant 1  
 
Definite integral of radical in denominator  
 
Definite integral of absolute value of a linear  Integral of the absolute value of a linear expression
 
Definite integral of absolute value of a quadratic  Integral of the absolute value of a quadratic expression
 

















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