What is the integral of 2e^{2x}cos(y) ?

The integral of 2e^{2x}cos(y) is e^{2x}cos(y)+C

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integral of 2e^{2x}cos(y)

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

e^{2 x} cos (y) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int e^{u} \frac{1}{2} d u

= 2 cos (y) \cdot \int e^{u} \frac{1}{2} d u

Take the constant out:

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

= 2 cos (y) \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

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

Substitute back

u = 2 x

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

Simplify

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

= e^{2 x} cos (y)

Add a constant to the solution

= e^{2 x} cos (y) + C

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