What is the integral of sqrt(e^{2x)+e^{2x}} ?

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

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integral of sqrt(e^{2x)+e^{2x}}

\int e^{2 x} + e^{2 x} d x

2 e^{x} + C

Solution steps

\int e^{2 x} + e^{2 x} d x

Simplify

e^{2 x} + e^{2 x} : 2 e^{x}

= \int 2 e^{x} d x

Take the constant out:

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

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

Use the common integral:

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

= 2 e^{x}

Add a constant to the solution

= 2 e^{x} + C

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