# 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

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- ?Lv 69 years agoBest 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)

- Anonymous9 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)

- Moise GunenLv 79 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)

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