Question

Find ∫e13dx

Answer 1

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Answer on Question #50924 – Math – Integral Calculus

Problem

Find $\mathrm{Je13dx}$

**Remark.** There is error in formatting. I suppose that we need to find $\int e^{13}dx$ or $\int_{1}^{3}edx$ or $\int_{1}^{3}e^{x}dx$. In all cases tables of integrals involving powers or exponential function are used. Besides, the second and the third cases require Newton-Leibnitz formula.

Solution

First case

$e^{13}$ is constant, so $\int e^{13}dx = e^{13}x + C$, where $C$ is an arbitrary real constant.

Second case

$e$ is constant, so $\int_{1}^{3}edx = ex|_{1}^{3} = e(3 - 1) = 2e$.

Third case

$$\int_{1}^{3} e^{x} dx = e^{x}|_{1}^{3} = e^{3} - e$$