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If intxlog(1+x^2)dx=A(x)cdotlog(1+x^2)+B...

If `intxlog(1+x^2)dx=A(x)cdotlog(1+x^2)+B(x)+c`, then

A

`A(x)=((1+x^2))/2`

B

`B(x)=((1+x^2))/2`

C

`A(x)=-((1+x^2))/2`

D

`B(x)=-((1+x^2))/2`

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The correct Answer is:
A, D
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PATHFINDER-INDEFINITE INTEGRATION-QUESTION BANK
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  2. int(dx)/(x(x^m+1)) is equal to

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  3. If intxlog(1+x^2)dx=A(x)cdotlog(1+x^2)+B(x)+c, then

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  4. int(dx)/(sinx+sqrt3cosx)

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  5. If int(sinx+sin^3x)/(cos2x)dx=lamdacosx+mulogabs(f(x))+c, then

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

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  7. If intsin(logx)dx=f(x)(sing(x)-cosh(x))+c, then

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  8. If int sin^-1sqrt(x/(1+x))dx=f(x) sin^-1sqrt(x/(1+x))-sqrtx+ (hog)(x)+...

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  9. Let f(x) be a polynomial satisfying f(0)=2, f'(0)=3 and f''(x)=f(x). A...

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  10. Let f(x) be a polynomial satisfying f(0)=2, f'(0)=3 and f''(x)=f(x). A...

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  11. Let n be a positive interger such that In=intx^nsqrt(a^2-x^2)dx Answer...

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  12. Let n be a positive interger such that In=intx^nsqrt(a^2-x^2)dx Answer...

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  13. Match List-I with List-II

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

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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. If int((cos8x-cos7x)/(1+2cos5x))dx=(sin3x)/a-(sin2x)/b+c then the last...

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  17. If int(1+cos8x)/(tan2x- cot2x)dx= acos8x +c, then find the value of a.

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  18. If int(x+(cos^-1 3x)^2)/sqrt(1-9x^2)dx=Asqrt(1-9x^2)+B(cos^-1 3x)^3+C,...

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  19. If int(sinx^8-cosx^8)/(1-2sinx^2cosx^2)dx= asin2x +c, then find the va...

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  20. Evaluate int(dx)/((2x-x^2)^(3//2))

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