What is the integral of 2ye^x ?

The integral of 2ye^x is 2ye^x+C

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integral of 2ye^x

\int 2 y e^{x} d x

2 y e^{x} + C

Solution steps

\int 2 y e^{x} d x

Take the constant out:

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

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

Use the common integral:

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

= 2 y e^{x}

Add a constant to the solution

= 2 y e^{x} + C