What is the integral from x to 2x of e^{2x+y} ?

The integral from x to 2x of e^{2x+y} is e^{2x}(e^{2x}-e^x)

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integral from x to 2x of e^{2x+y}

\int_{x}^{2 x} e^{2 x + y} d y

e^{2 x} (e^{2 x} - e^{x})

Solution steps

\int_{x}^{2 x} e^{2 x + y} d y

Simplify

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

= \int_{x}^{2 x} e^{y} e^{2 x} d y

Take the constant out:

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

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

Use the common integral:

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

= e^{2 x} [e^{y}]_{x}^{2 x}

Compute the boundaries:

e^{2 x} - e^{x}

= e^{2 x} (e^{2 x} - e^{x})

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\int_{1}^{4} \frac{ln ( x )}{x ^{6}} d x

\int_{1}^{16} x^{\frac{3}{2}} d x

\int_{0}^{2} [x^{2}] d x

What is the integral from x to 2x of e^{2x+y} ?
The integral from x to 2x of e^{2x+y} is e^{2x}(e^{2x}-e^x)