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1. ∫x^nlnx dx (n>0) with the limits e and 1:

u= lnx dv/dx=x^n
du/dx=1/x v=(x^n+1)/n+1

Using the formula for integration by parts, i get :
(lnx)((x^n+1)/n+1)-∫((x^n+1)/n+1)*(1/x)

i'm unsure as to how to integrate :

∫((x^n+1)/n+1)*(1/x)
2. m
(Original post by Chelsea12345)
∫x^nlnx dx (n>0) with the limits e and 1:

u= lnx dv/dx=x^n
du/dx=1/x v=(x^n+1)/n+1

Using the formula for integration by parts, i get :
(lnx)((x^n+1)/n+1)-∫((x^n+1)/n+1)*(1/x)

i'm unsure as to how to integrate :

∫((x^n+1)/n+1)*(1/x)
try setting u as the term containing n
actually this is wrong nvm
3. (Original post by Chelsea12345)
∫x^nlnx dx (n>0) with the limits e and 1:

u= lnx dv/dx=x^n
du/dx=1/x v=(x^n+1)/n+1

Using the formula for integration by parts, i get :
(lnx)((x^n+1)/n+1)-∫((x^n+1)/n+1)*(1/x)

i'm unsure as to how to integrate :

∫((x^n+1)/n+1)*(1/x)
if you take the 1/n+1 out of the integral (as it is just a constant) you end up with the integral of x^n+1/x which simplifies to the integral of x^n
4. (Original post by bruh2132)
if you take the 1/n+1 out of the integral (as it is just a constant) you end up with the integral of x^n+1/x which simplifies to the integral of x^n
the integral does simplify like you said to get :
lnx(x^n+1/n+1) -1/n+1 ∫x^n
which then becomes :
lnx(x^n+1/n+1) -1/n+1(x^n+1/n+1)

Applying the limits e and 1:
e^n+1/n+1 - e^n+1/(n+1)^2 + 1^n+1/(n+1)^2
multiplying this by(n+1) gives :
e^n+1 - e^n+1/n+1 + 1^n+1/n+1

how do i factrise this ^ to get the answer of ne^n+1 +1 /(n+1)^2
5. (Original post by Chelsea12345)
the integral does simplify like you said to get :
lnx(x^n+1/n+1) -1/n+1 ∫x^n
which then becomes :
lnx(x^n+1/n+1) -1/n+1(x^n+1/n+1)

Applying the limits e and 1:
e^n+1/n+1 - e^n+1/(n+1)^2 + 1^n+1/(n+1)^2
multiplying this by(n+1) gives :
e^n+1 - e^n+1/n+1 + 1^n+1/n+1

how do i factrise this ^ to get the answer of ne^n+1 +1 /(n+1)^2
well when I integrated I ended up with x^n+1( lnx/n+1 - 1/(n+1)^2)
6. E=Chelsea12345;75931760]the integral does simplify like you said to get :
lnx(x^n+1/n+1) -1/n+1 ∫x^n
which then becomes :
lnx(x^n+1/n+1) -1/n+1(x^n+1/n+1)

Applying the limits e and 1:
e^n+1/n+1 - e^n+1/(n+1)^2 + 1^n+1/(n+1)^2
multiplying this by(n+1) gives :
e^n+1 - e^n+1/n+1 + 1^n+1/n+1

how do i factrise this ^ to get the answer of ne^n+1 +1 /(n+1)^2[/QUOTE]

if you simplify at this point, you end up with
x^n+1(lnx/n+1 - 1/(n+1)^2) then put it over a common denominator and apply limits
7. (Original post by bruh2132)
E=Chelsea12345;75931760]the integral does simplify like you said to get :
lnx(x^n+1/n+1) -1/n+1 ∫x^n
which then becomes :
lnx(x^n+1/n+1) -1/n+1(x^n+1/n+1)

Applying the limits e and 1:
e^n+1/n+1 - e^n+1/(n+1)^2 + 1^n+1/(n+1)^2
multiplying this by(n+1) gives :
e^n+1 - e^n+1/n+1 + 1^n+1/n+1

how do i factrise this ^ to get the answer of ne^n+1 +1 /(n+1)^2
if you simplify at this point, you end up with
x^n+1(lnx/n+1 - 1/(n+1)^2) then put it over a common denominator and apply limits[/QUOTE]
thankyou

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