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Softaken PDF Watermark Permissions:

You are free to download and use Softaken PDF Watermark trial version as long as you are a registered user. Please understand that Softaken PDF Watermark Trial is a free to use but free to test software. That means you can use it before you decide to purchase the full version.Q:

An integral from Apostol’s Calculus volume 1

In Apostol’s Calculus volume 1, there is an integral like this:
$$\int_{0}^{\infty}\frac{x^2+1}{(1-e^{ -x})^2}dx$$
I don’t understand how to evaluate it?

A:

Here is how you can proceed:
$(1-e^{ -x})^2=1+2e^{ -x}+e^{ -2x}+2e^{ -2x}+e^{ -3x}+2e^{ -3x}+e^{ -4x}+\ldots$
then we have
$\int_0^\infty\frac{x^2+1}{(1-e^{ -x})^2}dx = \sum_{n=0}^\infty\int_0^\infty \frac{x^{2n}+1}{2^n}\,dx = \sum_{n=0}^\infty\frac{(2n)!}{2^{2n}n!(2n+1)} = \sum_{n=0}^\infty \frac{2^{2n}n!(2n)!}{(2n+1)!(2n+1)} = \frac{1}{2}\sum_{n=0}^\infty \frac{2^{2n}(n!)^2}{(2n+1)!}$
$= \frac{1}{2}\sum_{n=0}^\infty \frac{2^{2n}(2n)!}{(2n+1)(2n)!} = \frac{1}{2}\sum_{n=0}^\infty \frac{2^{2n}}{(2

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This software is a powerful image editor that is suited for individuals or professional photographers who want to improve their existing photographs.
Softaken Photo Editor functions like many other photo manipulation programs, but it offers a lot more customization options. Some of these are not found in any other photo editor software on the market.
This product’s impressive collection of features is due in part to its relatively easy-to-use GUI. It provides well-structured and easy-to-use options, and it offers convenient shortcuts for popular tasks.
The program allows you to edit your photos by using two different color modes. With color mode set to “Relative” you can apply various effects directly to the colors of the image.
The “Relative” color mode applies custom effects to the colors of your image. Softaken Photo Editor suggests these effects based on the colors in your image, and you can easily add, delete or modify them.
On the other hand, with the color mode set to “Absolute” you can apply filters or effects to the specific colors in your image.
Easily apply effects to your photos
Some of the more interesting effects that you can use include:
– Auto Tone: This filter automatically detects and adapts the colors in your image to give it a more balanced look. For instance, if you select a photo in which the colors appear too dark, the software will automatically adjust them to a brighter look.
– High Dynamic Range (HDR): This software adds a video-like dynamic range to your image, producing an overall more balanced image. In addition, it automatically colors the various areas in your image to help create a pleasant look.
– Lost Outdoor – Black & White: This filter helps you recover the dynamic range of your image so that all the colors are evenly visible. When you choose this mode, the software will automatically adjust your image using a color wheel.
– Lost Outdoor – Warm – Tonal: This filter recreates the colors of an outdoor image, making them slightly warmer. If you wish to save your final image, you can adjust the tonality settings to apply an additional final touch.
– Lost Outdoor – Warm – Black & White: This filter recreates the colors of an outdoor image, making them slightly warmer. If you wish to save your final image, you can adjust the tonality settings to apply an additional final touch.
– Night Photo: This filter simulates the effects of shooting your images in

Windows 10 – x64
MacOS 10.9 (MacBook pro)
Intel Core2 Duo 2.2GHz or higher
Minimum of 3.5GB RAM
NVIDIA GeForce 8400M GS or better
1 GB VRAM (recommended)
3GB VRAM (optional)
Notes:
Saving works best on your hard drive (not SSD)
Saving works best on full screen, and in windowed mode is possible but may result in laggy gameplay

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