Answer
349.2k+ views
Hint: The equation in the question is the simple type of integration that can be solved using some simple operation.
We can solve it by adding a term or number in the both numerator or denominator.
As well as we can solve it by rationalizing the denominator method.
Complete step by step solution:
Let us take the equation,
$ \Rightarrow $ $ \int {\dfrac{{3x}}{{3x - 1}}dx} $
By adding and subtracting $ 1 $ in both numerator and denominator,
$ \Rightarrow $ $ \int {\dfrac{{\left( {3x - 1} \right) + 1}}{{3x - 1}}} $
$ \Rightarrow \int {1dx + \int {\dfrac{{dx}}{{3x - 1}}} } $
By integrating and using logarithmic integration,
$ \Rightarrow x + \dfrac{1}{3}\log (3x - 1) + c $
So, the correct answer is “ $ x + \dfrac{1}{3}\log (3x - 1) + c $ ”.
Note:
> Integration is the calculation of an integral.
> The integration denotes the summation of discrete data. The integral is calculated to find the functions which will describe the area, displacement, volume, that occurs due to a collection of small data, which cannot be measured singularly.
We can solve it by adding a term or number in the both numerator or denominator.
As well as we can solve it by rationalizing the denominator method.
Complete step by step solution:
Let us take the equation,
$ \Rightarrow $ $ \int {\dfrac{{3x}}{{3x - 1}}dx} $
By adding and subtracting $ 1 $ in both numerator and denominator,
$ \Rightarrow $ $ \int {\dfrac{{\left( {3x - 1} \right) + 1}}{{3x - 1}}} $
$ \Rightarrow \int {1dx + \int {\dfrac{{dx}}{{3x - 1}}} } $
By integrating and using logarithmic integration,
$ \Rightarrow x + \dfrac{1}{3}\log (3x - 1) + c $
So, the correct answer is “ $ x + \dfrac{1}{3}\log (3x - 1) + c $ ”.
Note:
> Integration is the calculation of an integral.
> The integration denotes the summation of discrete data. The integral is calculated to find the functions which will describe the area, displacement, volume, that occurs due to a collection of small data, which cannot be measured singularly.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)