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int(sqrt(x^2+10 x+24))/(x+5)dx is equal ...

`int(sqrt(x^2+10 x+24))/(x+5)dx` is equal to

A

`sqrt(x^(2)+10x+24)+sec^(-1)(x+5)+c`

B

`sqrt(x^(2)+10x+24)-"cosec"^(-1)(x+5)+c`

C

`sec^(-1)(x+5)-sqrt(x^(2)+10x+24)+c`

D

`sqrt(x^(2)+10x+24)-sec^(-1)(x+5)+c`

Text Solution

Verified by Experts

The correct Answer is:
D
` I=int(sqrt(x^(2)+10x+24))/(x+5)dx=int(sqrt((x+5)^(2)-1))/(x+5)dx`
`"Put " x+5=sec theta implies dx=sec theta tan theta d theta `
`:. I=int(tan theta)/(sec theta)*sec theta tan theta d theta `
`=int(sec^(2) theta-1)d theta`
`=tan theta-theta+C`
`=sqrt(x^(2)+10x+24)-sec^(-1)(x+5)+c`
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CENGAGE PUBLICATION-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
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  4. The value of int(1+logx)/(sqrt((x^(x))^(2)-1))dx " is "

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  5. "If "int x^(5)(1+x^(3))^(2//3)dx=A(1+x^(3))^(8//3)+B(1+x^(3))^(5//3)+c...

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  6. Evaluate: int(sin2x)/(sin^4x+cos^4x)dx

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  7. int(x+2)/((x^2+3x+3)sqrt(x+1))dx is equal to 1/3tan^(-1)(x/(sqrt(3(x+1...

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  8. Evaluate the following Integrals : int (sec x .dx)/(sqrt(sin (2x+A...

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  9. int(cos2x)/((e^(-x)+cosx)sqrt(1+sin2x))dx,x in(0,(pi)/(2)) is equal t...

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  10. I=int(cos4x+1)/(cotx-tanx)dx is equal to ?

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  11. If int(dx)/(x^2(x^n+1)^((n-1)/n))=-(f(x))^(1/n)+C then f(x) is (...

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  14. int(3+2cosx)/((2+3cosx)^2)dx is equal to (a) ((sinx)/(3cosx+2))+c ...

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  15. "If " (d)/(dx)f(x)=f'(x), " then " int(xf'(x)-2f(x))/(sqrt(x^(4)f(x)))...

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  18. Ifint(dx)/(cos^3xsqrt(sin2x))=a(tan^2x+b)sqrt(tanx)+c ,t h e n a=(sq...

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  19. Evaluate: int dx/( (x + 2)(x^2 + 1) )

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  20. Ifint(3e^x-5e^(-x))/(4e^x+5e^(-x))dx=a x+bln(4e^x+5e^(-x))+C ,t h e n ...

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