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README.md

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@@ -59,68 +59,63 @@ The exercises solved in this repository cover indefinite integrals and are prese
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Below are the exercises solved in this repository. They have been written in LaTeX to ensure a clear and precise presentation. Feel free to use and improve the code as needed.
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### [Exercises: Find the following integrals]()
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### [Exercises: Find the following integrals]() 👇
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## [Exercicise A:]()
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### [Exercicise A:]()
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<br>
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${\huge \bf \int \left(x^{\frac{3}{2}} + 2x + 1\right) \, dx}$
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<br>
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- 💡 [**Solution:**: We can integrate each term separately:]()
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[**Solution:**: We can integrate each term separately:]()
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<br>
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$\huge \bf \int x^{\frac{3}{2}} \, dx + \int 2x \, dx + \int 1 \, dx$
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<br><br>
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<p align="center"> ────────────── ✦ ──────────────
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- [**1st:**]() ☞ $\huge \bf \int x^{\frac{3}{2}} dx$
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[**1st:**]()
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$\huge \bf \int x^{\frac{3}{2}} dx$
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<br>
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$$\huge \bf \frac{x^{\frac{3}{2} + 1}}{\frac{3}{2} + 1} \rightarrow \frac{x^{\frac{5}{2}}}{\frac{5}{2}} \rightarrow \frac{2}{5}x^{\frac{5}{2}}$$
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<br><br>
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- [**2st:**]() ☞ $\huge \bf \int 2x dx\$
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[**2st:**]() ☞ $\huge \bf \int 2x dx\$
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<br>
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$$\huge \bf \frac{x^{1+1}}{1+1} \rightarrow 2 \cdot \frac{x^2}{2} \rightarrow x^2$$
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<br><br>
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- [**3st:**]() ☞ $\huge \bf \int 1 dx$
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<br>
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[**3st:**]()
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$\huge \bf \int 1 dx$
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<p align="center"> The indefinite integral of \(1\) with respect to \(x\) is given by:
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<br>
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$$\huge \bf \int 1 \, dx \rightarrow x + k$$
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$\huge \bf \int 1 \, dx \rightarrow x + k$
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<br>
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<p align="center"> where \(k\) is the constant of integration.
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$$\huge \bf \ x + k$$
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$\huge \bf \ x + k$
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<br>
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### <p align="center"> [**Final Result:**]()
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[**Final Result:**]()
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<br>
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$$\huge \bf \int \left(x^{\frac{3}{2}} + 2x + 1\right) \, dx \rightarrow \frac{2}{5}x^{\frac{5}{2}} + x^2 + x + k$$
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<br>
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#
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## [Exercicise B:]()
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### [Exercicise B:]()
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$$\huge \bf \int \sqrt[3]{x^2} \, dx$$
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