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I guess you can find plenty of them in the Problem Department of the American Matematical Mathematical Monthly. For instance, here is a nice one by M. Hajja and P. Walker:

Evaluate $\displaystyle \int_{0}^{1}\int_{0}^{1} \int_{0}^{1} (1+u^{2}+v^{2}+w^{2})^{-2} du dv dw$.

Good thing about this one is that there may exist a CAS out there that does not give you the answer at once.

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I guess you can find plenty of them in the Problem Department of the American Matematical Monthly. For instance, here is a nice one by M. Hajja and P. Walker:

Evaluate $\displaystyle \int_{0}^{1}\int_{0}^{1} \int_{0}^{1} (1+u^{2}+v^{2}+w^{2})^{-2} du dv dw$.

Good thing about this one is that there may exist a CAS out there that does not give you the answer at once.

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I guess you can find plenty of them in the Problem Department of the American Matematical Monthly. For instance, here is a nice one by M. Hajja and P. Walker:

Evaluate $\displaystyle \int_{0}^{1}\int_{0}^{1} \int_{0}^{1} (1+u^{2}+v^{2}+w^{2})^{-2} du dv dw$.

Good thing about this one is that there may exist a CAS out there that doe does not give the answer at once.

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