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Find int(e^(x))/(sqrt(4-e^(2x)))dx...

Find `int(e^(x))/(sqrt(4-e^(2x)))dx`

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`I=int(e^(x))/(sqrt(4-e^(2x)))dx=int(e^(x))/(sqrt(2^(2)-(e^(x))^(2)))dx`
Let `e^(x)=t " or " e^(x)dx=dt`
`:. I=int(dt)/(sqrt(4-t^(2)))=int(dt)/(sqrt(2^(2)-t^(2)))`
`=sin^(-1)((t)/(2))+C=sin^(-1)((e^(x))/(2))+C`
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CENGAGE-INDEFINITE INTEGRATION-Question Bank
  1. Find int(e^(x))/(sqrt(4-e^(2x)))dx

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  2. Let k(x) = ((x^(2)+1))/(root(3)(x^(3)+3x+6) dx and k(-1) = 1/root (3)(...

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

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

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

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

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  8. (4+x^(12))/((x^(6)-2x^(3)+2))dx = x^(alpha)/alpha +x^(beta)/gamma+delt...

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

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

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  11. Let int cos^(3)xdx = m sin x +(sin^(3)x)/n+c, then n+2m is equal to

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  12. 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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  13. If int (e^x-1)/(e^x+1)dx=f(x)+C, then f(x) is equal to

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

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

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

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  17. 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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  18. 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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  19. Let f(x) be the primitive of (3x+2)/(sqrt(x-9))w.r.t. x. If F(10) = 60...

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

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

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