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I have completely forgotted how to integrate a trigonometric function with a power. for example: sin(x^3).
i think it requirs breaking into parts, like u = x^3, v = sin(u), or something like that, but my attempts have failed, and its been years since i have done this. Please help.
Regards
Mark
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Integrating sin(x^3) is extremely difficult. It involves complex numbers and the gamma function. Perhaps you mean sin(x)^3? This is much easier.
Edited to add: The technique you tried to use, u-substitution, can only be used when the derivative of "u" is also in your function.
sin(x^3)dx
u = x^3
du = 3*x^2dx
As you can see, du is not in the function. However, if your function was:
(3x^2)*sin(x^3)dx
Integration would be done by:
u = x^3
du = 3x^2dx
(3x^2)*sin(x^3)dx = sin(u)du
Integrating this would give you -cos(u), which would be -cos(x^3)
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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Now set
and then it's done.
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That would be a great solution, if the problem was integrating sin(x)^3. But it's sin(x^3).
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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Yeah, that's pretty much hard.
Anyway
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Yeah, that's pretty much hard.
Anyway
Wow r u serious? Those mathematicians have gone bonkers i tell u
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What is this two-variable Gamma?
Is it some extension to the original Euler Gamma?
IPBLE: Increasing Performance By Lowering Expectations.
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That's the incomplete Gamma function.
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