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## Homework Statement

∫x*cos(x^2) dx

I tried using integration by parts, but the integral of cos(x^2) is very long, and I couldn't get it completely with my knowledge at the moment, so is there an easier way to solve this problem?

- Thread starter Panphobia
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- #1

- 435

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∫x*cos(x^2) dx

I tried using integration by parts, but the integral of cos(x^2) is very long, and I couldn't get it completely with my knowledge at the moment, so is there an easier way to solve this problem?

- #2

Dick

Science Advisor

Homework Helper

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Yes, don't use integration by parts. Use u substitution. Put u=x^2.## Homework Statement

∫x*cos(x^2) dx

I tried using integration by parts, but the integral of cos(x^2) is very long, and I couldn't get it completely with my knowledge at the moment, so is there an easier way to solve this problem?

- #3

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So the definite integral [0, sqrt(pi)] would be 0 correct?

- #4

Mark44

Mentor

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Also, when you're working with integrals, it's usually best to see if a simple substitution will work before tackling it with integration by parts. Integration by substitution is usually a simpler approach that integration by parts, so if it doesn't work out, you haven't wasted much time.

In this case, and as you saw, it's a very obvious substitution that works.

BTW, when you post a problem, you need to show what you have tried, even if it wasn't successful. That's a rule in this forum.

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