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On- line integral calculator is a very useful tool for evaluating the integration of different functions. This tool

uses integration rules and formulas. One need to substitute the values only and it helps in finding the result

will automatically come out.

This tool is very effective and also helps in finding the solutions of typical problems even involving higher

exponents. It also helps in evaluating the integration of trigonometric functions involving different variables.

This can be understood by the following examples:-

**Example 1:- **

Find the integral of the below mentioned function:-

a) ∫x

**Solution 1:-**

uses integration rules and formulas. One need to substitute the values only and it helps in finding the result

will automatically come out.

This tool is very effective and also helps in finding the solutions of typical problems even involving higher

exponents. It also helps in evaluating the integration of trigonometric functions involving different variables.

This can be understood by the following examples:-

Find the integral of the below mentioned function:-

a) ∫x

Now here we have to find the d/dx f(x).

Here, f (x) = x.

Therefore,

∫f(x) = ∫x

= x^{2}/2 + c. (because integration ∫x^{n }= x^{n+1}/n+1 + c).

**Example 2:- **

Find the integration of the below mentioned function x^{2}+x+1

**Solution 2:- **

Let f (x) = x^{2}+x+1

Now here we have to find the integration of f(x).

Here, f (x) = x^{2}+x+1.

Therefore,

∫f(x) = ∫ (x^{2}+x+1)dx

= ∫(x^{2})dx + ∫(x)dx + ∫ (1)dx

= x^{2+1}/2+1 + x^{1+1}/1+1 + x + c (because integration of

Constant is 1).

= x^{3}/3 + x^{2}/2 + x + c (because d/dx (x^{n}) = n x^{n-1}

= x^{3}/3 + x^{2}/2 + x + c

Here, f (x) = x.

Therefore,

∫f(x) = ∫x

= x

Find the integration of the below mentioned function x

Let f (x) = x

Now here we have to find the integration of f(x).

Here, f (x) = x

Therefore,

∫f(x) = ∫ (x

= ∫(x

= x

Constant is 1).

= x

= x