Question: sin 2x – 4e^3x

Answer:

The anti derivative of sin 2x – 4e^3x is the function of x whose derivative is sin 2x – 4e^3x.

It is known that,

\begin{align} \frac {d}{dx} \left(-\frac{1}{2}cos 2x – \frac {4}{3} e^{3x}\right) = sin2x – 4e^{3x} \end{align}

Therefore, the anti derivative of (sin 2x – 4e^3x) is \begin{align} \left(-\frac{1}{2}cos 2x – \frac {4}{3} e^{3x}\right) \end{align}

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