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

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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