# int e^(4x)cos(2x) dx Find the indefinite integral

int e^(4x)cos(2x)dx

To solve, apply integration by parts int u dv = u*v - int vdu .

In the given integral, the let the u and dv be:

u = e^(4x)

dv = cos(2x)dx

Then, take the derivative of u to get du. Also, take the integral of dv to get v.

du = e^(4x)*4dx

du = 4e^(4x)dx

intdv = int cos(2x)dx

v = (sin(2x))/2

Substituting them to the integration by parts formula yields

int e^(4x)cos(2x)dx= e^(4x)*(sin(2x))/2 - int (sin(2x))/2 * 4e^(4x)dx

int e^(4x)cos(2x)dx= (e^(4x)sin(2x))/2 - int 2e^(4x)sin(2x)dx

For the integral at the right side, apply integration by...

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