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Math Help - How do i solve this integral problem?

  1. #1
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    Question How do i solve this integral problem?

    Im totally confused about the following problem. please help me to solve it and explain. following is the complete question:

    Find and simplify te derivitive of

    f(x) = (x+2) log e(x+2)

    hence evaluate,

    2
    ∫ x log e(x + 2) dx
    1


    (note: that is "log to the base e" in everywhere that the "e" is mentioned )

    Thanks in advance!
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  2. #2
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    log of base e is just ln?
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  3. #3
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    Quote Originally Posted by da_coolest View Post
    Im totally confused about the following problem. please help me to solve it and explain. following is the complete question:

    Find and simplify te derivitive of

    f(x) = (x+2) log e(x+2)

    hence evaluate,

    2
    ∫ x log e(x + 2) dx
    1


    (note: that is "log to the base e" in everywhere that the "e" is mentioned )

    Thanks in advance!
    Product rule. f'= 2x log(x^2+ 2)+ (x^2+ 2)\frac{1}{x^2+2}(2x) = 2x log(x^2+ 2)+ 2x
    Now you know, from the "Fundamental Theorem of Caclulus" that
    2\int x log(x^2+ 2)dx+ 2\log x dx= (x^2+2)log(x^2+ 2)+ C
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