PyPDF2 import PdfReader

Load and read the uploaded PDF file

pdf_path = '/mnt/data/1735633350103lrtvtonp.pdf' reader = PdfReader(pdf_path)

Extract text from the first page of the PDF (assuming the integrals are on this page)

page = reader.pages[0] text = page.extract_text() text[:1000] # Show the first 1000 characters for reviewIt seems the extracted text from the PDF is not in a readable format, possibly due to encoding issues. Let me try a different approach to analyze the content.

I'll attempt to extract the images or any other readable components from the PDF to assist with solving the integrals. Let's try extracting images from the PDF to see if the integrals are provided in that form import fitz # PyMuPDF

Open the PDF using PyMuPDF

doc = fitz.open(pdf_path)

Extract images from the first page of the document

images = [] for page_num in range(len(doc)): page = doc.load_page(page_num) image_list = page.get_images(full=True) for img_index, img in enumerate(image_list): xref = img[0] img_data = doc.extract_image(xref) images.append(img_data["image"])

Checking how many images were extracted

len(images)The PDF contains 27 images. It is likely that the integrals are included in one or more of these images.

I will now proceed to analyze the images and identify the integrals to solve. Let me extract and display one of the images for further analysis. Let's extract one image to visually check its content from PIL import Image import io

Get the first image extracted

image_data = images[0] image = Image.open(io.BytesIO(image_data))

Display the image

image.show()It seems I attempted to display the image, but there was no output. Let me instead save the image and present it in a way that allows us to analyze it effectively. Save the first image extracted to a file image_path = '/mnt/data/integral_image.png' image.save(image_path)

Provide the path to the image for download or review

image_pathIt seems like I can’t do more advanced data analysis right now. Please try again later.

Let me know if you'd like to proceed in a different way or if you have any other questions!