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Evaluate integral e^5 x + 8 / e^5 x dx. a. x - 8 / 5 e^-5 x + c. b. x + 8 / 5 e^5 x + c. c. 1 - 8...

Question:

Evaluate {eq}\displaystyle \int \dfrac {e^{5 x} + 8} {e^{5 x}}\ dx {/eq}.

a. {eq}\displaystyle x - \dfrac 8 5 e^{-5 x} + c {/eq}.

b. {eq}\displaystyle x + \dfrac 8 5 e^{5 x} + c {/eq}.

c. {eq}\displaystyle 1 - \dfrac 85 e^{-5 x} + c {/eq}.

d. {eq}\displaystyle 1 + \dfrac 8 5 e^{5 x} + c {/eq}.

Integration of Exponentials:

An exponential function written in the dneominator of a rational function such as {eq}\dfrac{1}{e^{px}} {/eq} and we need its anti-derivative. Then, we may try to rewrite this expression with a negative exponent and solve the integration using the common formula shown below:

{eq}\int e^{-px}\ dx=\dfrac{e^{-px}}{-p}+C {/eq}

  • Where {eq}C {/eq} is the constant of integration.

Answer and Explanation: 1

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Given:

{eq}\displaystyle \int \dfrac{e^{5 x} + 8} {e^{5 x}}\ dx=?\\[2ex] {/eq}

Rewrite the above rational function as,

{eq}\begin{align*} \int\fr...

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Integration Problems in Calculus: Solutions & Examples

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Chapter 13 / Lesson 13
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Learn what integration problems are. Discover how to find integration sums and how to solve integral calculus problems using calculus example problems.


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