Find the integral.

{eq}\displaystyle \int (e^{2 x} - 1) dx {/eq}.

Question:

Find the integral.

{eq}\displaystyle \int (e^{2 x} - 1) dx {/eq}.

U-Substitution:

One of the many techniques that we can use to solve for an integral would be{eq}u {/eq}-substitution. With {eq}u {/eq}-substitution, we will use the variable {eq}\displaystyle u {/eq} to represent a variable. One should also get the derivative of the said variable. However, we still need to swith it back to the original variable used.

Answer and Explanation: 1

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{eq}\begin{align} \displaystyle & \int (e^{2 x} - 1) dx\\ & \int e^{2 x} dx - \int 1 dx\\ & \int e^{2 x} dx - x\\ \end{align} {/eq}

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How to Solve Integrals Using Substitution

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Chapter 13 / Lesson 5
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Explore the steps in integration by substitution. Learn the importance of integration with the chain rule and see the u-substitution formula with various examples.


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