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

?

Answer 1

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

Answer 2

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)
?

Answer 3

yep

Answer 4

ln(x) * x^7/7 - ∫ (x^7/7)(1/x)
ln(x)* x^7/7 - x^8/56 * ln(x) + C
?

Answer 5

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

Answer 6

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.

Answer 7

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

Answer 8

correct

Answer 9

ty