How do you integrate int x^3ln(5x)∫x3ln(5x) by integration by parts method?

1 Answer
Andrea S.
Dec 30, 2016

int x^3ln(5x)dx = x^4/4(ln(5x)-1/4)∫x3ln(5x)dx=x44(ln(5x)−14)

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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