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

\int 15 sec^{5} (x) d x

\frac{d}{d x} (cos (x) (sin (x)))

\int_{0}^{\frac{π}{12}} cos (6 x) d x

\int_{0}^{2} x 3^{x} 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