Antiderivative Calculator

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Anti-derivative, also known as Integration is the reverse process of differentiation. Graphically, anti-derivative of a function gives the area covered by the graph of the function with respect to the X-axis, if it is integrated with respect to the ‘x’ in the function. Anti-derivative calculator is the online tool which can easily give the anti-derivative value of a given function.

Example 1: Find the anti-derivative of the function, f(x) = x2 – 7.

The Power Rule of Integration says that ∫ (x) n dx = x (n+1)/ (n+1) + c
where ‘c’ is a constant.

Using the above formula we get the anti-derivative as: ∫ f(x) dx = x2+1/ (2+1) – 7x + c

This gives: ∫ f(x) dx = x3/ 3– 7x + c.

Example 2: Find the anti-derivative of the function, f(x) = (1/x2) + x2

The Power Rule of Integration says that ∫ (x) n dx = x (n+1)/ (n+1) + c
where ‘c’ is a constant.

The above function can also be written as: f(x) = x-2 + x2.

This gives: ∫ f(x) dx = x-2+1/ (-2+1) + x2+1/ (2+1) + c

∫ f(x) dx = (x-1/ -1) + x3/ 3 + c.

f(x) dx = -x-1 + x3/3 + c which can also be written as:∫ f(x) dx = -(1/x)+ x3/3 + c


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