What is the integral of e^xcos(2)e^x ?

The integral of e^xcos(2)e^x is 1/2 cos(2)e^{2x}+C

Popular >

integral of e^xcos(2)e^x

\int e^{x} cos (2) e^{x} d x

\frac{1}{2} cos (2) e^{2 x} + C

Solution steps

\int e^{x} cos (2) e^{x} d x

Take the constant out:

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

= cos (2) \cdot \int e^{x} e^{x} d x

Apply exponent rule:

a^{n} \cdot b^{n} = (a \cdot b)^{n}

e^{x} e^{x} = (ee)^{x}

= cos (2) \cdot \int (ee)^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= cos (2) \frac{( ee ) ^{x}}{ln ( ee )}

Simplify

cos (2) \frac{( ee ) ^{x}}{ln ( ee )} : \frac{1}{2} cos (2) e^{2 x}

= \frac{1}{2} cos (2) e^{2 x}

Add a constant to the solution

= \frac{1}{2} cos (2) e^{2 x} + C

\int \frac{cos ( a ) x}{1 - sin ( a ) x} d x

\int \frac{x}{( 2 x - 1 )} d x

\int \frac{x + 5}{x + 4} d x

\int (x^{2} + 8) (x - 8) d x

\int 6^{x} sin (6^{x}) d x

What is the integral of e^xcos(2)e^x ?
The integral of e^xcos(2)e^x is 1/2 cos(2)e^{2x}+C