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I need help with - Integral Calculus - JEE Main-11

Find the integral \int (3x +4)^{3} dx

  • Option 1)

    \frac{(3x+4)^{3}}{3} + c

  • Option 2)

    \frac{(3x+4)^{4}}{3} + c

  • Option 3)

    \frac{(3x+4)^{5}}{3} + c

  • Option 4)

    \frac{(3x+4)^{2}}{3} + c

 
Answers (1)
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G gaurav

As we have learnt,

 

Extended forms of fundamental formulae -

If x is replaced by a LINEAR FUNCTION of x\Rightarrow \left ( ax+b \right ) form then ,

\int f\left ( ax+b \right )dx =\frac{F\left ( ax+b \right )}{\frac{\mathrm{d} }{\mathrm{d} x}\left ( ax+b \right )}+c

- wherein

Fundamental formulae such as   \int x^{n}dx=\frac{x^{n+1}}{n+1}  , \int sinx dx=-cosx,..... and so on 

 

 \int (3x +4)^{3} dx = \frac{3x +4)^{4}}{3} + c

 


Option 1)

\frac{(3x+4)^{3}}{3} + c

Option 2)

\frac{(3x+4)^{4}}{3} + c

Option 3)

\frac{(3x+4)^{5}}{3} + c

Option 4)

\frac{(3x+4)^{2}}{3} + c

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