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Let us consider the integral of the foll...

Let us consider the integral of the following forms
`f(x_(1), sqrt(mx^(2)+nx+p))^(1//2)`
Case I If `m gt 0`, then put `sqrt(mx^(2)+nx+C)=u pm x sqrt(m)`
Case II If `p gt 0`, then put `sqrt(mx^(2)+nx+C)=u x pm sqrt(p)`
Case III If quadratic equation `mx^(2)+nx+p=0` has real roots `alpha` and `beta` there put `sqrt(mx^(2)+nx+p)=(x-alpha) u ` or `(x-beta)u`
`int ((x+sqrt(1+x^(2)))^(15))/(sqrt(1+x^(2))) dx` is equal to

A

`sqrt(9x^(2)+4x+6)=u pm 3x`

B

`sqrt(9x^(2)+4x+6)=3u pm x`

C

`x=1/t`

D

`9x^(2)+4x+6=1/t`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • Let us consider the integral of the following forms f(x_(1), sqrt(mx^(2)+nx+p))^(1//2) Case I If m gt 0 , then put sqrt(mx^(2)+nx+C)=u pm x sqrt(m) Case II If p gt 0 , then put sqrt(mx^(2)+nx+C)=u x pm sqrt(p) Case III If quadratic equation mx^(2)+nx+p=0 has real roots alpha and beta there put sqrt(mx^(2)+nx+p)=(x-alpha) u or (x-beta)u To evaluate int(dx)/((x-1)sqrt(-x^(2)+3x-2)) one of the most suitable substitution could be

    A
    `sqrt(-x^(2)+3x-2)=u`
    B
    `sqrt(-x^(2)+3x-2)=(ux sqrt(2))`
    C
    `sqrt(-x^(2)+3x-2)=u(1-x)`
    D
    `sqrt(-x^(2)+3x-2)=u(x+2)`

  • If p and q are roots of the quadratic equation x^(2) + mx + m^(2) + a = 0 , then the value of p^(2) + q^(2) + pq , is

    A
    0
    B
    a
    C
    `-a`
    D
    `+- m^(2)`

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