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

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

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

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

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

Solution steps

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

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 z} d z - \int_{0}^{1000} 5 d z

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

\int_{0}^{1000} 5 d z = 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}

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

\int_{- 2}^{5} (x^{2} + 6 x + 8) d x

\int_{4}^{\infty} ln (x) d x

\int_{n}^{2 n} \frac{1}{x} d x

\int_{0}^{5} x^{2} + 3 x + 1 d x

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