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Integrate (x+1)sqrt(2x^2+3)...

Integrate `(x+1)sqrt(2x^2+3)`

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To solve the integral \(\int (x+1)\sqrt{2x^2+3} \, dx\), we can break it down into two parts: 1. \(\int x\sqrt{2x^2+3} \, dx\) 2. \(\int \sqrt{2x^2+3} \, dx\) Let's denote these integrals as \(I_1\) and \(I_2\) respectively. Therefore, we can express the original integral as: \[ ...
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Knowledge Check

  • Integral of f(x)=sqrt(1+x^2) with respect to x^2 is

    A
    `2/3((1+x^2)^(3//2))/x+C`
    B
    `2/3x(1+x^2)^(3//2)+C`
    C
    `2/3(1+x^2)^(3//2)+C`
    D
    None of these

  • Integration of (1)/(sqrt(x^(2)=9)) with respect to (x^(2)+1) is equal to

    A
    `sqrt(x^(2)+9)+C`
    B
    `-(1)/(sqrt(x^(2)+9))+C`
    C
    `2sqrt(x^(2)+9)+C`
    D
    none of these

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