∫ u dv = uv - ∫ v du

∫ x^6 ln x dx

u = x^6
du = 6x^5
dv = ln x
v = x ln(x) - x

x^6(x ln(x) - x) - ∫ (x ln(x) - x) 6x^5

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Question

∫ u dv = uv - ∫ v du

∫ x^6 ln x dx

u = x^6
du = 6x^5
dv = ln x
v = x ln(x) - x

x^6(x ln(x) - x) - ∫ (x ln(x) - x) 6x^5

?

anonymous · Answer

you could do it that way. A simplier approach is to let u = ln(x) and dv = x^6

shamil98 · Answer

Ok.
so

∫ x^6 ln x dx

u = ln x
dv = x^6
du = 1/x
v = x^7/7

ln(x) * x^7/7 - ∫ (x^7/7)(1/x) 
?

anonymous · Answer

yep

shamil98 · Answer

ln(x) * x^7/7 - ∫ (x^7/7)(1/x) 
ln(x)* x^7/7 - x^8/56 * ln(x) + C
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anonymous · Answer

∫ (x^7/7)(1/x) dx = (1/7)∫x^6 dx = (1/49)x^7

shamil98 · Answer

oh.
ln(x) * x^7/7 - ∫ (x^7/7)(1/x) 
ln(x) * x^7/7 - ∫ x^6/7
ln(x) * x^7/7 - ∫ (x^7/49
my bad didnt simplify that part.

shamil98 · Answer

ln(x) * x^7/7 - x^7/49 + C **

anonymous · Answer

correct

shamil98 · Answer

ty