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Assuming you mean natural logs (as 'log' by itself means logs to any base):
∫ln x dx = x ln x - x + C
let y = ln x → ey = x → ey dy = dy
→ ∫ln x dx = ∫y ey dy
But ∫uv = u∫v - ∫u'∫v
let u = y → u' = 1
let v = ey
→ ∫y ey dy = y∫ey dy - ∫∫ ey dy
= y ey - ey + C
= (ln x) x - x + C
= x ln x - x + C
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∙ 11y ago
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