How do I evaluate $\int e^{6 x} cos 5 x d x$ $int e^{6x} cos 5x dx$ ?

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How do I evaluate $\int e^{6 x} cos 5 x d x$ $int e^{6x} cos 5x dx$ ?

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Answer 1 · 2015-03-09T00:55:31

I would use Integration by Parts, twice: enter image source here
Now you use a trick...taking the integral on the right to the left of the $=$ $=$ sign:

Finally the integral gives you:
$\int e^{6 x} cos (5 x) d x = \frac{e^{6 x}}{61} \cdot [6 cos (5 x) + 5 sin (5 x)] + c$ $inte^(6x)cos(5x)dx=e^(6x)/61*[6cos(5x)+5sin(5x)]+c$

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How do I evaluate $\int e^{6 x} cos 5 x d x$ $int e^{6x} cos 5x dx$ ?

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