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Integration is a very important concept in mathematical calculus. Integration means finding the anti-derivative of the given function. Therefore integration of a function f(x) is ‘F(x)’ where f(x) is the derivative of the function F(x). The online tool used to find the integration of a function is called as integration calculator.

Given is the function f(x) = (5 - x)

Now integration of the function gives F(x)

F(x) = ∫f(x) dx = ∫(5 - x )

here let u = 5 -x; du = -dx ; dx = -du

Now substitution gives -∫(u)

Now u = 5 –x (-1/7)(5 - x)

Given is the function f(x) = 3 cos(2x);

Now integration of the function gives F(x)

F(x) = ∫f(x) = ∫3 cos(2x);

Here if u = 2x du = 2dx dx = du/2

Now substitution gives 3/2∫cosu du

Hence è3/2∫cosu du = 3/2 sin(u)

Now u = 2x; 3/2sin2x.