Question

5. [latex s=2]{ sin\quad 2x-4e }^{ 3x }[/latex]

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Answer 1

Solution:

The anti derivative e^2x is the function of x whose derivative is e^2x.

It is known that,

$\frac{d}{dx} (e^2^x)=2e^2^x\\\\=> e^2^x= \frac{1}{2} \frac{d}{dx} (e^2^x)$

∴ $Therefore\: , the\: anti\: derivative\: of\: e^2^x\: is\: \frac{1}{2} e^2^x.$

Answer 2

Answer:

The anti derivative e^2x is the function of x whose derivative is e^2x.

It is known that,

$\begin{gathered}\frac{d}{dx} (e^2^x)=2e^2^x\\\\= > e^2^x= \frac{1}{2} \frac{d}{dx} (e^2^x)\\\\\end{gathered}</p><p>$

∴

$Therefore\: , the\: anti\: derivative\: of\: e^2^x\: is\: \frac{1}{2} e^2^x.$