# What is the integrationof  ?

Melina

Solution:

Concept:The integration of a function   is the reciprocal of derivative of the function. It is denoted by  .

The anti-derivative of some functionsare given in the table below:

Calculation:

Step:1 The function to be integrated is  .

Step:2 From the Table 1, the integration expression is solved by using the integration of constant value 1 as x and integration of  as  .

Step:3 Hence, the integration of  is  .

Answer:The value of integration  is  .

Similar Problems:

Problem 1:What is anti-derivative of ?

Solution:

Step:1 From the Table 1, it is observed the anti-derivative of  is  .

Since anti-derivative is the reciprocal of derivative, the derivative of   must be  .

Verify the result by taking derivative of   as shown below:

Let the function be y such that  .

Step:2 Now take the derivative of the above equation.

Step:3 Simplify further to solve for the derivate as shown below:

Hence, the result obtained from the table is verified and anti-derivative of  is  .

Problem 2:What is anti-derivative of  ?

Solution:

Step:1  From the Table 1, it is observed the anti-derivative of  is  .

Since anti-derivative is the reciprocal of derivative, the derivative of   must be  .

Verify the result by taking derivative of   as shown below:

Let the function be y such that  .

Step:2 Now take the derivative of the above equation.

Step:3 Simplify further to solve for the derivate as shown below:

Hence, the result obtained from the table is verified and anti-derivative of  is \.

Answer: The anti-derivative of  is  .

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