Integration of : ((Inx^2)^4) divided by x)dx?

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Answer 1 · 2018-04-29T02:20:27

$int(lnx^2)^4/xdx=16/5(lnx)^5+C$

.

$int(lnx^2)^4/xdx=int(2lnx)^4/xdx=16int(lnx)^4*1/xdx=16I$

Let $u=lnx$

$du=1/xdx$

Let's substitute;

$I=intu^4du=1/5u^5+C$

Let's substitute back:

$I=1/5(lnx)^5+C$

$int(lnx^2)^4/xdx=16/5(lnx)^5+C$