## Problem Statement

Calculate the definite integral:

$$
\int_{1}^{8} \frac{5 \sqrt{x+24}}{(x+24)^{2} \cdot \sqrt{x}} d x
$$
## Solution

![](https://cdn.mathpix.com/cropped/2024_05_22_cd7234dbad9f370b4719g-14.jpg?height=365&width=1219&top_left_y=797&top_left_x=110)

$=\int_{2}^{5} \frac{240 t^{2} dt}{576 \cdot t^{4}}=\frac{15}{36} \int_{2}^{5} t^{-2} dt=-\left.\frac{15}{36 t}\right|_{2} ^{5}=-\frac{15}{36}\left(\frac{1}{5}-\frac{1}{2}\right)=\frac{1}{8}$

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Source — "http://pluspi.org/wiki/index.php/\�\�\�\�\�\�\�\�\�\�\�\�_\�\�\�\�\�\� \%D0\%BD\%D0\%B5\%D1\%86\%D0\%BE\%D0\%B2_\%D0\%98\%D0\%BD\%D1\%82\%D0\%B5\%D0\%B3\%D1\%80\%D0\%B0\%D0\%BB $\%$ D1\%8B_11-9"

Categories: In the form of a scan | Kuznetsov's Problem Book Integrals Problem 11 | Integrals

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## Problem Kuznetsov Integrals 11-10

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