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int(0)^((pi)/(4))(dx)/(a^(2)cos^(2)x+b^(...

`int_(0)^((pi)/(4))(dx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)=(1)/(ab)tan^(-1).(b)/(a)(a,bge0)`

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int_(0)^((pi)/2)( dx)/((a^2cos^2x+b^2sin^2x)^2)=(pi)/(4).(a^(2)+b^(2))/(a^(3)b^(3))

int_(0)^(2pi)sin^(4).(x)/(2)cos^(5).(x)/(2)dx=0

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CHHAYA PUBLICATION-DEFINITE INTEGRAL -LONG ANSWER TYPE QUESTIONS
  1. int(2)^(5)sqrt((x-2)(5-x))dx=(9pi)/(8)

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  2. int(8)^(15)(dx)/((x-3)sqrt(x+1))=(1)/(2)log.(5)/(3)

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  3. int(0)^((pi)/(4))(dx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)=(1)/(ab)tan^(-1).(...

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  4. int(0)^((pi)/(2))(dx)/(2+cosx)=(pi)/(3sqrt(3))

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  5. int(2)^(3)(dx)/(sqrt(6x-x^(2)-5))=(pi)/(6)

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  6. int(0)^(2a)sqrt(2ax-x^(2))dx=(pia^(2))/(2)

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  7. Prove that , int(0)^(1)(dx)/(x^(2)+4x+5)=tan^(-1).(1)/(7)

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  8. int(1)^(2)(dx)/(sqrt(x^(2)+x-2))=log3

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  9. int(e)^(e^(2))(logxdx)/((1+logx)^(2))=(e)/(6)(2e-3)

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  10. int(0)^((pi)/(2))(sinxdx)/((2-cosx)(3+cosx))=(1)/(5)log.(8)/(3)

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  11. int(0)^((pi)/(2))(cosxdx)/((1+sinx)(2+sinx)(3+sinx))=(1)/(2)log.(32)/(...

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  12. int((1)/(9))^((1)/(4))(dx)/((1-x)sqrt(x))=log.(3)/(2)

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  13. int(7)^(23)(dx)/((x-2)sqrt(x+2))=(1)/(2)log.(15)/(7)

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  14. int(0)^((pi)/(2))(dx)/(4+5cosx)=(1)/(3)log2

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  15. int(0)^((pi)/(2))(dx)/(2cosx+4sinx)=(1)/(sqrt(5))log((3+sqrt(5))/(2))

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  16. int(0)^((pi)/(2))(dx)/(a+bcosx)(agtb)=(2)/(sqrt(a^(2)-b^(2)))tan^(-1)s...

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  17. int((pi)/(6))^((pi)/(3))(dx)/(sin^(4)xcos^(2)x)=(80sqrt(3))/(27)

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  18. int(a)^(b)(logx)/(x)dx=(1)/(2)log(ab)log((b)/(a))

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  19. int(0)^(1)x.sqrt((1-x^(2))/(1+x^(2)))dx=(pi-2)/(4)

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  20. int(1)^(2)(dx)/((x+1)sqrt(x^(2)-1))=(1)/(sqrt(3))

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