How do I evaluate #int e^{6x} cos 5x dx#?

Answer 1

I would use Integration by Parts, twice: Finally the integral gives you:
#inte^(6x)cos(5x)dx=e^(6x)/61*[6cos(5x)+5sin(5x)]+c#

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Answer 2

Christopher Agresta

To evaluate the integral ∫e^(6x) * cos(5x) dx, you can use integration by parts. Let u = e^(6x) and dv = cos(5x) dx. Then, differentiate u and integrate dv to find du and v. Afterward, apply the integration by parts formula:

∫u dv = uv - ∫v du

Substitute the values of u, v, du, and dv into the formula and solve the integral.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.