A couple questions on integration

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SUMMARY

This discussion focuses on solving two specific integration problems: the definite integral of x^4(ln3x) from 3 to 8 and the indefinite integral of 27x^2(cos(3x)). The recommended approach for the first integral involves substitution with y=3x followed by integration by parts. For the second integral, the use of substitution is suggested, although the specific substitution method is not detailed. Overall, integration by parts is emphasized as a key technique for these problems.

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antiflag403
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Hey everyone,
I've been having a little trouble with a few HW questions. If you guys could point me in the direction (ie- help me find the method to solve) I would really appreciate it. The q's are:
1. The definite integral from 3 to 8 of- x^4(ln3x)dx
For this one I am not sure wether I should make a substitution of y=3x and then do integration by parts or if there is an easier method.
2. The indefinite integral of- 27x^2(cos(3x))
Again I think that a substitution may be necessary although I can't seem to figure out what it is.
Thanks to anyone who can help me out!
Thanks
 
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HINT: Try integration by parts. :)
 

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