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

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

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

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

2

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{0}^{l n (3)} e^{2 x} d x = 4

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

= 4 - 2

Simplify

= 2

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