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

The integral of (e^xcos(x)) is (e^xsin(x))/2+(e^xcos(x))/2+C

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integral of (e^xcos(x))

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

\frac{e ^{x} sin ( x )}{2} + \frac{e ^{x} cos ( x )}{2} + C

Solution steps

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

Apply Integration By Parts

: e^{x} sin (x) - \int e^{x} sin (x) d x

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

Apply Integration By Parts

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

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

Take the constant out:

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

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

Therefore

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

Isolate

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

= \frac{e ^{x} sin ( x )}{2} + \frac{e ^{x} cos ( x )}{2}

Add a constant to the solution

= \frac{e ^{x} sin ( x )}{2} + \frac{e ^{x} cos ( x )}{2} + C

x \to 2 lim (x (x - 1))

x, 2

\int cos (2 ln (x)) d x

\int (- \frac{2}{11 - 11 x ^{2}}) d x

What is the integral of (e^xcos(x)) ?
The integral of (e^xcos(x)) is (e^xsin(x))/2+(e^xcos(x))/2+C