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integrate for me? (1 Viewer)
- Thread starter baby_pea
- Start date
I assume you're talking about ∫ (lnx)<sup>2</sup>dx in which case use integration by parts where:
u = (lnx)<sup>2</sup> , u' = 2lnx/x
v'= 1 , v=x
∫ 1.(lnx)<sup>2</sup>dx
= x(lnx)<sup>2</sup> - 2∫ lnx dx (then use integration by parts again on lnx where u = lnx)
= x(lnx)<sup>2</sup> - 2( xlnx - 2∫dx)
= 2x - 2xlnx + x(lnx)<sup>2</sup> + C
u = (lnx)<sup>2</sup> , u' = 2lnx/x
v'= 1 , v=x
∫ 1.(lnx)<sup>2</sup>dx
= x(lnx)<sup>2</sup> - 2∫ lnx dx (then use integration by parts again on lnx where u = lnx)
= x(lnx)<sup>2</sup> - 2( xlnx - 2∫dx)
= 2x - 2xlnx + x(lnx)<sup>2</sup> + C
