How Do You Integrate cos(sqrt x)?

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In summary, "tough integration problems" refer to challenging computational or mathematical problems that involve integrating multiple complex components from different fields to find a solution. These problems are difficult to solve because they require a deep understanding of each component and their interactions. Examples of tough integration problems in science include predicting climate change, understanding the human brain, and developing new medicines. Scientists can approach solving these problems by breaking them down into smaller components and collaborating with experts from different fields. The potential benefits of solving tough integration problems include gaining a deeper understanding of complex systems, developing new technologies and innovations, and finding solutions to pressing issues, potentially leading to scientific breakthroughs and advancements.
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mathrocks
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Does anyone know how to integrate cos(sqrt x) ?? I know the answer, i need to know the steps to do it?

Thanks
 
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Let [itex]u= \sqrt{x}= x^{\frac{1}{2}}[/itex]. Then [itex]du= \frac{1}{2}x^{-\frac{1}{2}}dx[/itex] so that [itex]dx= 2x^{\frac{1}{2}}du= 2udu[/itex].

[itex]\int{cos(\sqrt{x})dx}= \int{2u cos(u)du}[/itex].

Now use integration by parts.
 
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  • #3
let [tex] \sqrt{x} = y [/tex] be the variable substution and integrate by parts.
 
  • #4
as I was typing, HallsofIvy gopt it down first...
 

1. What is a "tough integration problem"?

A "tough integration problem" refers to a computational or mathematical problem that involves integrating multiple complex components, often from different fields or disciplines, to find a solution. This can be challenging because it requires a deep understanding of each component and how they interact with each other.

2. Why are tough integration problems difficult to solve?

Tough integration problems are difficult to solve because they often involve a large number of variables and complex relationships between them. This can make it challenging to find a unified solution that satisfies all the components involved.

3. What are some examples of tough integration problems in science?

Examples of tough integration problems in science can include predicting climate change, understanding the human brain, or developing new medicines. These problems require integrating data and knowledge from multiple fields such as physics, biology, and chemistry to find a comprehensive solution.

4. How can scientists approach solving tough integration problems?

Scientists can approach solving tough integration problems by breaking down the problem into smaller, more manageable components and then integrating them together. This can involve collaboration with experts from different fields, using advanced computational techniques, and continuously testing and refining the solution.

5. What are some potential benefits of solving tough integration problems?

The potential benefits of solving tough integration problems include gaining a deeper understanding of complex systems, developing new technologies and innovations, and finding solutions to some of the world's most pressing issues. Solving tough integration problems can also lead to new scientific breakthroughs and advancements in various fields.

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