# What is the integration of ?  Yesenia

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 Let the value equal to t then the value of in terms of is calculated as, Step:2 Substitute t for and for dx in the integral value as shown below: Step:3 From the Table 1, the integration expression is solved as, Step:4 Back substitute the value t as and simplify the above expression. 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 .

Answer:The 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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