What is the integral from 0 to 1 of e^{5x}-e^{4x} ?

The integral from 0 to 1 of e^{5x}-e^{4x} is (4e^5-5e^4+1)/(20)

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integral from 0 to 1 of e^{5x}-e^{4x}

\int_{0}^{1} e^{5 x} - e^{4 x} d x

\frac{4 e ^{5} - 5 e ^{4} + 1}{20}

Decimal

16.08309 \dots

Solution steps

\int_{0}^{1} e^{5 x} - e^{4 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}^{1} e^{5 x} d x - \int_{0}^{1} e^{4 x} d x

\int_{0}^{1} e^{5 x} d x = \frac{e ^{5} - 1}{5}

\int_{0}^{1} e^{4 x} d x = \frac{e ^{4} - 1}{4}

= \frac{e ^{5} - 1}{5} - \frac{e ^{4} - 1}{4}

Simplify

\frac{e ^{5} - 1}{5} - \frac{e ^{4} - 1}{4} : \frac{4 e ^{5} - 5 e ^{4} + 1}{20}

= \frac{4 e ^{5} - 5 e ^{4} + 1}{20}

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What is the integral from 0 to 1 of e^{5x}-e^{4x} ?
The integral from 0 to 1 of e^{5x}-e^{4x} is (4e^5-5e^4+1)/(20)