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Powers, Substitutions, Definite Integral, Constant of Integration, Absolute Value

Integration


Indefinite Integrals


Powers:


Integration of a linear factor Integral of a linear factor
 Integration of a fractional power Integration of a fractional power
 Integral of a positive fractional power Integral of a positive fractional power
 Integration of a reciprocal of a 4th root  Integration of a reciprocal of a 4th root
 Integral 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 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 times a radical
 Integral of a quadratic over a radical Integral of a quadratic over a radical

 

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Substitution:


 Integral of u*du  Integral of u*du
  Integration of : constant needed  Integral of a power: constant needed
 Integral of u^n * u'dx with a factor x missing Integral of u^n * u'dx with a factor x missing
 Integral of a root of a quantity, with u' present 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: 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 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: 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: Polynomial to a power, constant needed
 Integration of un*du: Reciprocal of a radical, 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 un*du and determination of the constant
 Integration of f '' and f ' and determination of the constants 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: Positive area under a linear function via geometry and definite integral
 Negative area and 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: 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: Positive area and a quadratic function via geometry and definite integral
 Negative 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:
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 odd fractional power, symmetric limits
 Definite Integral of Mixed Powers, symmetric limits definite integral of mixed fractional powers, symmetric limits
 Definite Integral of a Quadratic over a Fractional Power definite integral of quadratic over fractional powers
 Definite Integral of the reciprocal of (a radical times a power) definite integral of reciprocal of (a radical times a power
  Definite integral of a linear factor in quadrants 4 and 1  Definite integral of a linear factor in quadrants 4 and 1
 Definite integral of a quadratic, 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 a negative power in quadrant 1
  Definite integral of radical in denominator  Definite integral of radical in denominator
 

Definite integrals: Absolute VAlue


Definite integral of absolute value of a linear  Integral of the absolute value of a linear expression
 
 Definite integral of absolute value of an offset linear  Integral of the absolute value of an offset linear expression
 
 Definite integral of absolute value of a quadratic  Integral of the absolute value of a quadratic expression
 
 Definite integral of absolute value of a cubic  Integral of the absolute value of a cubic expression
 
 Definite integral of absolute value of a cosine  Integral of the absolute value of a cosine expression
 
















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