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Finding antiderivatives essentially involves "un-doing" the derivative. If the function you are antidifferentiating involves variables raised to a power, instead of multiplying by the power and decreasing the degree by one as you would do when taking the derivative, you add one to the degree of the power and multiply by the reciprocal of the new power .
For example, if the function you are antidifferentiating is x^2, you add one to the power (so now it is x^3) and multiply by the power's reciprocal (1/3). The antiderivative is (1/3)x^(3) plus an arbitrary constant.
If the function you are antidifferentiating involves sin and cos functions, use trig identities, partial fractions, u substitution, etc. Remember that you can always take the derivative of the expression you find as the antiderivative to verify its validity.
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Is there any other anti derivative of 1 divided by x?
The antiderivative of 1/x is ln(x) + C. That is, to the natural (base-e) logarithm, you can add any constant, and still have an antiderivative. For example, ln(x) + 5. These are the only antiderivatives; there are no different functions that have the same derivatives. This is valid, in general, for all antiderivatives: if you have one antiderivative of a function, all other antiderivatives are obtained by adding a constant.
What do integrate mean?
In calculus, "to integrate" means to find the indefinite integrals of a particular function with respect to a certain variable using an operation called "integration". Synonyms for indefinite integrals are "primitives" and "antiderivatives". To integrate a function is the opposite of differentiating a function.
What are the different uses of integration calculator?
Integral calculators calculate definite and indefinite integrals (antiderivatives) for use in calculus, trigonometry, and other mathematical fields/formulations.
How can you write a function that represents all possible antiderivatives of a given function?
Given a function f(x) find any anti-derivative, F(x). The set of all possible derivatives is obtained by adding a term not involving x which can take any value. So F(x) + C is a general derivative, where C can take any value.
How is calculus connected to foods?
Well, you can use antiderivatives to find the volume of a pear or ring donut, by rotating a curve (or 2 for the donut) about a line. You can have problems stating how many french fries are produced at an amusement park and how many are eaten per hour, and figure out the average rate that they are eaten, or the instantaneous rate at a given time (most likely higher around lunch and dinner times rather than when the park first opens) using derivatives.
