# Describe Methods of Integration.

Integration is a very interesting and important topic related to calculus. The geometric meaning of integration is that it represents the area under a curve. This is also one of the important applications of integrations. Let's discuss methods of integration here.

## Answer: The methods of integration include Integration by Substitution, Integration by Parts, Integration by Partial Fractions.

Let's understand in detail.

**Explanation:**

The three methods of integration are:

**Integration by parts**: This method is used when the function is in the form of the product of two different functions. For example, the integral of x sin x, and x^{2}cos x can be solved using integration by parts. We use the product of their derivatives and antiderivatives to calculate the integrals.

We use the formula ∫u(x).v(x) dx = u(x) ∫v(x) dx - ∫[u'(x). ∫v(x)] dx; to solve the integration of product of functions.

For example, for x sin x, we can take u(x) = x and v(x) = sin x, and solve the problem using the given formula.

We get the solution to be; -x cos x + sin x + C.

**Integration by partial fractions**: This method is used when the function is in the form of fractions. For example, 1/{(x - 3)(x - 4)} can be solved using integration by partial fractions.

If we want to solve the above problem, we first rearrange the problem in the form k/(x - a) - h/(x - b). By doing that, we get 1/{(x - 3)(x - 4)} = 1/(x - 4) - 1/(x - 3).

Now, we apply the integral identity of ∫1/x dx = ln |x| + C to get the final solution. The final result of the example above is; ln |x - 4| - ln |x - 3| + C.

**Integration by Substitution**: This method includes the substitution of a particular portion of the given function so as to make the problem simpler.

Also, there are some other special methods that can be used to calculate integrals of specific functions.

For example, integral of the function of the form e^{x }(f(x) + f'(x)), where f'(x) is derivative of f(x).