integrate e^2xcos2xsin3x dx

asked by guest
on Dec 25, 2024 at 11:56 pm



You asked:

Evaluate the integral: \(\int{{e}^{2} x \cos\left( 2 x \right) \sin\left( 3 x \right)}dx\)

MathBot Answer:

Antiderivative

\[\int{{e}^{2} x \cos\left( 2 x \right) \sin\left( 3 x \right)}dx = \left(- \frac{12 \cos{\left(3 x \right)} \sin{\left(2 x \right)}}{25} + \frac{13 \cos{\left(2 x \right)} \sin{\left(3 x \right)}}{25} - \frac{3 x \cos{\left(2 x \right)} \cos{\left(3 x \right)}}{5} - \frac{2 x \sin{\left(2 x \right)} \sin{\left(3 x \right)}}{5}\right) e^{2} + C\]

\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).

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