s asked in Science & MathematicsMathematics · 9 years ago

integration maths core 3?

hya im stuckon the integration question for core 3 maths

find the integral of 1+x divided by xsquared

also for the integral between 1 and 3

thanks a lot for your help

also the ansew in the book says 2/3 +ln3

Update:

thanks everyone for your ansews

4 Answers

Relevance
  • ?
    Lv 6
    9 years ago
    Best Answer

    The integrand can be written: 1/x^2 + x/x^2 which = x^(-2) + 1/x. The antiderivative is:

    -x^(-1) + ln(x) (from 1 to 3) = [-(3)^(-1) + ln(3)] - [-(1)^(-1) + ln(1)]..........ln(1) = 0, so

    -(1/3) + ln(3) - (-1) = 2/3 + ln(3)

  • Anonymous
    9 years ago

    integral of (1+x)/x^2 = Ln x -(1/x) + C (Between 1 and 3)

    ( Ln3 -(1/3) +C) - (Ln1-(1/1)+C) ===> But We Know Ln1=0

    Ln3-(1/3)+(1/1) = Ln3 +(2/3)

  • 9 years ago

    F(x) = ∫(1+x)/x^2 dx = ∫1/x^2 dx + ∫ 1/x dx = -1/x+ Ln(x) +C

    Value = F(3)-F(1) = -1/3 +Ln(3) +1/1 - Ln(1) = 2/3 + Ln(3)

  • JOS J
    Lv 7
    9 years ago

    -(1/x) + Log[x]

    2/3 + Log[3]

Still have questions? Get your answers by asking now.