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37 changes: 16 additions & 21 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -59,68 +59,63 @@ The exercises solved in this repository cover indefinite integrals and are prese

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.

### [Exercises: Find the following integrals]()
### [Exercises: Find the following integrals]() 👇

## [Exercicise A:]()
### [Exercicise A:]()

<br>

${\huge \bf \int \left(x^{\frac{3}{2}} + 2x + 1\right) \, dx}$

<br>

- 💡 [**Solution:**: We can integrate each term separately:]()
[**Solution:**: We can integrate each term separately:]()

<br>

$\huge \bf \int x^{\frac{3}{2}} \, dx + \int 2x \, dx + \int 1 \, dx$

<br><br>
<p align="center"> ────────────── ✦ ──────────────

- [**1st:**]() ☞ $\huge \bf \int x^{\frac{3}{2}} dx$
☟ [**1st:**]()

$\huge \bf \int x^{\frac{3}{2}} dx$

<br>

$$\huge \bf \frac{x^{\frac{3}{2} + 1}}{\frac{3}{2} + 1} \rightarrow \frac{x^{\frac{5}{2}}}{\frac{5}{2}} \rightarrow \frac{2}{5}x^{\frac{5}{2}}$$

<br><br>

- [**2st:**]() ☞ $\huge \bf \int 2x dx\$
[**2st:**]() ☞ $\huge \bf \int 2x dx\$

<br>

$$\huge \bf \frac{x^{1+1}}{1+1} \rightarrow 2 \cdot \frac{x^2}{2} \rightarrow x^2$$

<br><br>

- [**3st:**]() ☞ $\huge \bf \int 1 dx$

<br>
[**3st:**]()
$\huge \bf \int 1 dx$

<p align="center"> The indefinite integral of \(1\) with respect to \(x\) is given by:

<br>

$$\huge \bf \int 1 \, dx \rightarrow x + k$$
$\huge \bf \int 1 \, dx \rightarrow x + k$

<br>

<p align="center"> where \(k\) is the constant of integration.

$$\huge \bf \ x + k$$
$\huge \bf \ x + k$

<br>

### <p align="center"> [**Final Result:**]()
[**Final Result:**]()

<br>

$$\huge \bf \int \left(x^{\frac{3}{2}} + 2x + 1\right) \, dx \rightarrow \frac{2}{5}x^{\frac{5}{2}} + x^2 + x + k$$

<br>

#

## [Exercicise B:]()
### [Exercicise B:]()

$$\huge \bf \int \sqrt[3]{x^2} \, dx$$

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