What is the integral from 0 to 1000 of e^{4x}-5 ?

The integral from 0 to 1000 of e^{4x}-5 is -20001/4+e^{4000} 1/4

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integral from 0 to 1000 of e^{4x}-5

\int_{0}^{1000} e^{4 x} - 5 d x

- \frac{20001}{4} + e^{4000} \frac{1}{4}

Solution steps

\int_{0}^{1000} e^{4 x} - 5 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}^{1000} e^{4 x} d x - \int_{0}^{1000} 5 d x

\int_{0}^{1000} e^{4 x} d x = \frac{1}{4} (e^{4000} - 1)

\int_{0}^{1000} 5 d x = 5000

= \frac{1}{4} (e^{4000} - 1) - 5000

Simplify

\frac{1}{4} (e^{4000} - 1) - 5000 : - \frac{20001}{4} + e^{4000} \frac{1}{4}

= - \frac{20001}{4} + e^{4000} \frac{1}{4}

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What is the integral from 0 to 1000 of e^{4x}-5 ?
The integral from 0 to 1000 of e^{4x}-5 is -20001/4+e^{4000} 1/4