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    ∫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)
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    (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
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    (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
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    (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
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    (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)
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    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
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    (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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