How do you integrate #int x^3ln(5x)# by integration by parts method?

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How do you integrate #int x^3ln(5x)# by integration by parts method?

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Answer 1 · 2016-12-30T17:24:15

#int x^3ln(5x)dx = x^4/4(ln(5x)-1/4)#

Explanation:

#int x^3ln(5x)dx = int ln(5x) d(x^4/4) = x^4/4ln(5x) - int x^4/4 d(ln(5x)) = x^4/4ln(5x) - int x^4/4 1/xdx = x^4/4ln(5x)-int x^3/4dx=x^4/4ln(5x)- x^4/16dx=x^4/4(ln(5x)-1/4)#

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How do you integrate #int x^3ln(5x)# by integration by parts method?

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