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If f(x) =sqrt(x-1),g(x)=e^(x) and intfog...

If `f(x) =sqrt(x-1),g(x)=e^(x)` and `intfog(x)dx=Afog(x)+Btan^(-1)(fogx)+C` then `A^(3)+B^(2)` equals:

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To solve the problem step by step, we will follow the instructions provided in the video transcript. ### Step 1: Define the Functions We are given two functions: - \( f(x) = \sqrt{x - 1} \) - \( g(x) = e^x \) ### Step 2: Find \( f(g(x)) \) ...
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RESONANCE ENGLISH-INDEFINITE INTEGRATION -SINGLE AND DOUBLE VALUE INTEGER TYPE
  1. If f(x) = int(2sinx-sin2x)/(x^(3))dx, where xne0, then Limit(xto0) f^(...

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  2. If int sin^4 x cos^4 x dx=1/128 [ax-sin4x+1/8 sin8x]+c then a=

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

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  4. If int(sqrt(4+x^2))/(x^6)dx = ((a+x^2)^(3/2).(x^2-b))/(120x^5)+C the...

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  5. For a gt 0,if I= int sqrt((x)/(a ^(3) -x ^(3)))dx =A sin ^(-1) ((x ^(3...

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  6. If int x/sqrt(1+x^2+sqrt((1+x^2)^3)dx= ksqrt(1+sqrt(1+x^2))+c. find k

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  7. If inte^(sinx).(xcos^(3)x-sinx)/(cos^(2)x)dx=e^(sinx)f(x)+C, such that...

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  8. Let g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0. then the value of 8g(...

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  9. If f(x) =sqrt(x-1),g(x)=e^(x) and intfog(x)dx=Afog(x)+Btan^(-1)(fogx)+...

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  10. If int(2sin2phi-cosphi)/(6-cos^(2)phi-4sinphi)dphi=p" ln "|sin^(2)phi-...

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  11. if int (x-1)^2/(x^4+x^2+1)dx=1/sqrta tan^-1 ((x^2-1)/(xsqrt3))-b/sqrta...

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  12. If int(1+xcosx)/(x(1-x^(2)e^(2sinx)))dx = k" ln "sqrt((x^(2)e^(2 sinx)...

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  13. If int (x^4 + 1)/(x(x^2+1)^2)\ dx = A ln |x| +B/(1+x^2)+C, then A+B eq...

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  14. If int 1/(1-sin^4x)dx=1/(asqrtb)+tan^(- 1)(sqrt(a)tanx)+1/btanx+C the...

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  15. If int(cos^(3)x+cos^(5)x)/(sin^(2)x+sin^(4)x)dx=p sinx-q/(sinx)-rtan^(...

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  16. If int(dx)/(sqrt(sin^(3)xcos^(5)x))=a sqrt(cot x)+bsqrt(tan^(3)x)+c, t...

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