What is the integral of e^xcos(n)x ?

The integral of e^xcos(n)x is cos(n)(e^xx-e^x)+C

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integral of e^xcos(n)x

\int e^{x} cos (n) x d x

cos (n) (e^{x} x - e^{x}) + C

Solution steps

\int e^{x} cos (n) x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cos (n) \cdot \int e^{x} x d x

Apply Integration By Parts

= cos (n) (e^{x} x - \int e^{x} d x)

\int e^{x} d x = e^{x}

= cos (n) (e^{x} x - e^{x})

Add a constant to the solution

= cos (n) (e^{x} x - e^{x}) + C

What is the integral of e^xcos(n)x ?
The integral of e^xcos(n)x is cos(n)(e^xx-e^x)+C