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If `(In(ex^(x+1))+(In x^(sqrtx)))^(2)/(1+(x In x)(In e^(2)x^(x)))dx = f(x)+C`, where f(1) =0`, then `e^(e^(f(2)-1))is equal to

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CENGAGE-INDEFINITE INTEGRATION-Question Bank
  1. If int dx/(1+sqrt(x+1)+sqrt(x) ) = ax + bsqrtx+c int sqrt((x+1)/x)dx t...

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

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

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

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

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

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

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

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  10. 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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  11. 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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  12. Let int (4+3x)/(x^(3)-2x-4)= In|(x-k)/(sqrt(x^(2)+kx+1))|+C, then k^(2...

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

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

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  15. 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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  16. If int ((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-1/(f(x)) where f(x) is of t...

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  17. Let f(x) be the primitive of (3x+2)/(sqrt(x-9))w.r.t. x. If F(10) = 60...

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  18. If int (Insqrtx)/x dx = g(x)+Cwhere g(1) = 0, then g(e^(6)) is equal ...

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  19. int(sin^(2)x)/(sec^(2)x-cos^(2)x) dx = lambda x - 1/mu tan^(-1)((tanx)...

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  20. If int e^(x)((x+2)/(x+4))^(2) dx = e^(x)((x-alpha)/(x+beta))+C where C...

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