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There are two functions inside the integral symbol, one is related to the independent variable and the other is independent of the independent variable.

Both are the derivative and Tload is a constant.

How to get the result of integration? enter image description here

The correct result should be like this

enter image description here

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    $\begingroup$ Make use of coordinates: e.g. Integrate[Cross[{t1'[x], t2'[x], t3'[x]}, {a1, a2, a3}], x] works. $\endgroup$
    – user64494
    Jan 12, 2020 at 13:39
  • $\begingroup$ Thank you for your answers. Yes, it works. But it is not general. Are there any other ways that can integrate the derivative of an undefined function? $\endgroup$
    – Yang Liu
    Jan 12, 2020 at 18:12

1 Answer 1

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You can get pretty close by taking the cross out of the integral and use indefinite integration, then apply your limits.

$\left(\int tc'(\xi ) T{\text{load}} \, d\xi \right)\times u'(s)$

as

f[ξ_] = Cross[Integrate[Tload tc'[ξ], ξ], u'[s]]
(*Cross[Tload*tc[ξ], u'[s]]*)

Then apply the limits

f[L] - f[s]

Cross[Tload*tc[L], u'[s]] - Cross[Tload*tc[s], u'[s]]

Mathematica will not further simplify without knowing more about the functions involved.

Older versions of Mathematica such as M8 will do definite integrals of derivatives, but newer versions are more careful, since if the integrand is not continuous, blindly applying limits will often end up with an incorrect result.

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  • $\begingroup$ Thanks so much for your answers! It helps a lot. $\endgroup$
    – Yang Liu
    Jan 12, 2020 at 23:24

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