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The value of int0^x (t - abst)^2/(1 + t^...

The value of `int_0^x (t - abst)^2/(1 + t^2) dt` is equal to

A

`4(x - tan^-1 x),` if ` x lt 0`

B

0 , if `x gt 0`

C

`In ( 1+x^2)`, if `x gt 0`

D

None of these

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The correct Answer is:
A, B
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PATHFINDER-INDEFINITE INTEGRATION-QUESTION BANK
  1. If I = int (sin x + sin^3 x)/(cos 2x) dx = A cos x + B log abs(f(x)) +...

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  2. If int (xe^x)/(sqrt(1 + e^x)) dx = f(x) sqrt(1 + e^x) - 2 In g(x) + c...

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  3. The value of int0^x (t - abst)^2/(1 + t^2) dt is equal to

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  4. int dx/((x+1)(x+2)) = A log (x + 1) + B log (x +2) + c where

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  5. Let f(x) = 3/( 3x^2 + 9) and g(x)=x^2/( 3x^2 + 9) int (f(x) + g(x)) ...

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  6. Let f(x) = 3/( 3x^2 - 9) and g(x)=x^2/( 3x^2 - 9) int (g(x) - f(x)) ...

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  7. If i(m - 2 , n + 2) = int sin^(m - 2)x cos^(n+2)x dx and I(m,n) = - (s...

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  8. If In = int x sin^n x dx and In = -(x sin^(n-1)x cos x)/n + (sin^n x)/...

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  9. Match List - I with List-II Let the functions defined in List - I ha...

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  10. Match List - I with List-II Let the functions defined in List - I ha...

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  11. If int xdx/sqrt(7x - 10 - x^2)^3 = (lambda(7x - 20))/sqrt(7x - 10 - x^...

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  12. If int dx/(1 + sin x) = tan(x/2 + a) + b then the value of -(16a)/pi m...

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  13. If int sin^-1 ((2x + 2)/sqrt(4x^2 + 8x + 13)) dx = (x + 1) tan^-1 ((2x...

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  14. If int (x^9 + x^6 + x^3)(2x^6 + 3x^3 + 6)^(1/3) dx = 1/a (2x^9 + 3x^6 ...

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  15. If int (sqrttanx + sqrtcotx) dx = a tan^-1 ((tan x - 1)/sqrt(b tan x))...

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  16. Evaluate : int dx/(7x - 10 - x^2)

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  17. Evaluate : int (xdx)/sqrt(1+x^4)

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  18. Evaluate : int dx/(sqrte^(5x) cdot root(4)(e^(2x) + e^(-2x))^3)

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  19. Evaluate : int0^log5(e^x(e^x-1)^(1/2))/(e^x+3)dx

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  20. Evaluate : int1^2 (e^(x^2))dx=a, then find the value of inte^(e^4)root...

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