5 = 5X
-cos(3x) + constant
The integral of 0 is some constant C. You can solve for this constant by using boundry conditions if there are any given; otherwise, just put C.
An indefinite integral has an arbitrary constant. The arbitrariness ensures that the integral of any function has infinitely many values.
-cos x + Constant
The indefinite integral of sin 2x is -cos 2x / 2 + C, where C is any constant.
The integral of ln(2) is a constant multiple of x times the natural logarithm of 2, plus a constant of integration. In other words, the integral of ln(2) with respect to x is x * ln(2) + C, where C is the constant of integration. This integral represents the area under the curve of the natural logarithm of 2 function with respect to x.
-cos(x) + constant
The integral of a given function between given integration limits will always be a constant. The integral of a given function between variable limits - for example, from 0 to x - can only be a constant if the function is equal to zero everywhere.
-cos(3s)+C, where C is some arbitrary constant
The integral of a constant, such as 5, with respect to a variable (usually denoted as ( x )) is expressed as ( \int 5 , dx = 5x + C ), where ( C ) is the constant of integration. This result represents a family of functions that have a slope of 5, indicating that for every unit increase in ( x ), the value of the integral increases by 5.
∫ ax dx = ax/ln(a) + C C is the constant of integration.
There are two types of integrals: definite and indefinite. Indefinite integrals describe a family of functions that differ by the addition of a constant. Definite integrals do away with the constant and evaluate the function from a lower bound to an upper bound.