What is the integral from 0 to ln(2) of e^{x+2y} ?

The integral from 0 to ln(2) of e^{x+2y} is e^{2y}

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integral from 0 to ln(2) of e^{x+2y}

\int_{0}^{l n (2)} e^{x + 2 y} d x

e^{2 y}

Solution steps

\int_{0}^{l n (2)} e^{x + 2 y} d x

Simplify

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

= \int_{0}^{l n (2)} e^{x} e^{2 y} d x

Take the constant out:

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

= e^{2 y} \cdot \int_{0}^{l n (2)} e^{x} d x

Use the common integral:

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

= e^{2 y} [e^{x}]_{0}^{l n (2)}

Compute the boundaries:

1

= e^{2 y} \cdot 1

Simplify

= e^{2 y}

\frac{\partial}{\partial x} (2 x \cdot e^{x y})

\frac{\partial}{\partial x} (x^{2} z + 3 z^{2} x + 6 (x + z))

\frac{d}{d x} (2 x^{6} - 8 x^{5} + 10 x^{4} - 10 x^{2} + 8 x - 2)

\int \frac{x - 4}{x ^{2} + 2 x - 15} d x

x \to \infty lim (3 x - 9 x^{2} + 6 x)

What is the integral from 0 to ln(2) of e^{x+2y} ?
The integral from 0 to ln(2) of e^{x+2y} is e^{2y}