What is the integral from 0 to ln(2) of e^{2x}(5-e) ?

The integral from 0 to ln(2) of e^{2x}(5-e) is (5-e) 3/2

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integral from 0 to ln(2) of e^{2x}(5-e)

\int_{0}^{l n (2)} e^{2 x} (5 - e) d x

(5 - e) \frac{3}{2}

Decimal

3.42257 \dots

Solution steps

\int_{0}^{l n (2)} e^{2 x} (5 - e) d x

Take the constant out:

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

= (5 - e) \cdot \int_{0}^{l n (2)} e^{2 x} d x

\int_{0}^{l n (2)} e^{2 x} d x = \frac{3}{2}

= (5 - e) \frac{3}{2}

What is the integral from 0 to ln(2) of e^{2x}(5-e) ?
The integral from 0 to ln(2) of e^{2x}(5-e) is (5-e) 3/2