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If f(x) = int((1+x)(1-x+x^(2))(1+x+x^(2)...

If `f(x) = int((1+x)(1-x+x^(2))(1+x+x^(2))+x^(2))/(1+2x+3x^(2)+4x^(3)+3x^(4)+2x^(5)+x^(6)) dx` then find the value of [F(99)-F(3)].[Note :[k] denotes greatest integer less than or equal to k.]

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CENGAGE-INDEFINITE INTEGRATION-Question Bank
  1. Let k(x) = ((x^(2)+1))/(root(3)(x^(3)+3x+6) dx and k(-1) = 1/root (3)(...

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  2. If f(x) = int((1+x)(1-x+x^(2))(1+x+x^(2))+x^(2))/(1+2x+3x^(2)+4x^(3)+3...

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  3. If f(x) = int2e^(x) cos^(2)x(-tan^(2)x+tanx+1)dx and f(x) passes throu...

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  4. If int (cosec^(2)x)/((cosec x + cot x)^(9/2)) dx = (cosec x - cot x)^(...

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  5. intsin4x e^(tan^(2)x)dx = c-A cos^(4)x.e^(tan^(2)x) then A is equal to

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  6. If int dx/(1+sqrt(x+1)+sqrt(x) ) = ax + bsqrtx+c int sqrt((x+1)/x)dx t...

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  7. (4+x^(12))/((x^(6)-2x^(3)+2))dx = x^(alpha)/alpha +x^(beta)/gamma+delt...

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  8. let f(x) =int (4+x^(12))/(x^(4)+x^(3)-7x^(2)-4x+16)dx = A/sqrt3 tan^(-...

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  9. If curve f(x) = int x^(1)(2x^(3)+3x+4)^(3)(1+x+x^(3))dx passes through...

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  10. If f(x) =(3(Inx)^(2)+(In x)^(4))/(x(1+(In x)^(2)-(Inx)^(3))^(2))dx and...

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  11. If (sqrt(e^(7x)))/(root (4)(e^(2x)+e^(-2x)))dx = 1/k(e^(n)+1)^(beta/ga...

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  12. If int(log(ex)e)(log(e^(2)x)e)(log(e^(3)x)e)dx/x = Alog |1+logx|+B log...

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  13. Let int cos^(3)xdx = sin x +(sin^(3)x)/m + (sin^(5)x)/n+c, then n+2m i...

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  14. If (In(ex^(x+1))+(In x^(sqrtx)))^(2)/(1+(x In x)(In e^(2)x^(x)))dx = f...

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  15. If int (x^(6)+7x^(5)+6x^(4)+5x^(3)+4x^(2)+3x+1)e^(x)dx is equal to sum...

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  16. int ((x^(6)-4)dx)/((x^(6)+2)^(1/4)x^(4)) = (1(x^(6)+2)^(m))/x^(n)+C, t...

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  17. Let int (4+3x)/(x^(3)-2x-4)= In|(x-k)/(sqrt(x^(2)+kx+1))|+C, then k^(2...

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  18. If int (x^(8)-12x^(4)+4)/(x^(4)-4x^(2)+2)dx = x^(a)/a + (4x^(b))/b +2x...

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  19. Suppose A = int dx/(x^(2)+6x+25) and B= int dx/(x^(2)-6x-27). If 12(...

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  20. Let int dx/(x^(2008)+x) = 1/p In((x^(q))/(1+x^(r)))+C where p,q,r in N...

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