integrate e^2xcos2xsin3x dx

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



You asked:

Evaluate the integral: ∫e2xcos⁡(2x)sin⁡(3x)dx\int{{e}^{2} x \cos\left( 2 x \right) \sin\left( 3 x \right)}dx

MathBot Answer:

Antiderivative

∫e2xcos⁡(2x)sin⁡(3x)dx=(−12cos⁡(3x)sin⁡(2x)25+13cos⁡(2x)sin⁡(3x)25−3xcos⁡(2x)cos⁡(3x)5−2xsin⁡(2x)sin⁡(3x)5)e2+C\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

ee is Euler's number, a mathematical constant that is approximately 2.718282.71828.

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