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  • Confused! kindly explain, - Integral Calculus - JEE Main-15

Find the integral \int (2x+3)^{2}dx

  • Option 1)

    \frac{(2x+3)^{3}}{2}+ C

  • Option 2)

    \frac{(2x+3)^{3}}{3}+ C

  • Option 3)

    \frac{(2x+3)^{3}}{6}+ C

  • Option 4)

    none of these

Answers (1)

best_answer

As we have learned

Type of integration by substitution -

\int (ax+b)^{n}f(x)dx

or    \int\frac{f(x)}{(ax+b)^{n}}dx

- wherein

Where n is any rational number. (+ive or -ive)

Let (ax+b)=t

\therefore dx=\frac{dt}{a} .

 

Put 2x+3= t 

\Rightarrow 2dx = dt

\Rightarrow dx = dt/2

\Rightarrow \int t^{2}\frac{dt}{2}= \frac{t^{3}}{6}+ C= \frac{(2x+3)^{3}}{6}+ C 

 

 

 

 

 


Option 1)

\frac{(2x+3)^{3}}{2}+ C

This is incorrect

Option 2)

\frac{(2x+3)^{3}}{3}+ C

This is incorrect

Option 3)

\frac{(2x+3)^{3}}{6}+ C

This is correct

Option 4)

none of these

This is incorrect

Posted by

Aadil

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