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Integrate the functions tan^(-1)sqrt((...

Integrate the functions
`tan^(-1)sqrt((1-x)/(1+x))`

Text Solution

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The correct Answer is:
`(1)/(2)x. cos^(-1)x-(1)/(2) sqrt(1-x^(2))+c`
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KUMAR PRAKASHAN-INTEGRALS -MISCELLANEOUS EXERCISE-7
  1. Integrate the functions (2+sin2x)/(1+cos2x)e^(x)

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  2. Integrate the function is Exercise. (x^(2)+x+1)/((x+1)^(2)+(x+2))

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  3. Integrate the functions tan^(-1)sqrt((1-x)/(1+x))

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  4. Integrate the function is (xcos^-1x)/sqrt(1-x^2)

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  5. Evaluate the definite integrals int(pi/2)^(pi)e^(x)((1-sinx)/(1-cosx...

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  6. Evaluate the definite integrals int(0)^(pi/4)(sinxcosx)/(cos^(4)x+si...

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  7. Evaluate the definite integrals in exercise. overset((pi)/(2)) under...

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  8. Evaluate the definite integrals in exercise. overset((pi)/(3)) under...

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  9. Evaluate the definite integrals int(0)^(1)(dx)/(sqrt(1+x)-sqrtx)

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  10. Evaluate the definite integrals int(0)^(pi/4)(sinx+cosx)/(9+16sin2x)...

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  11. Evaluate the definite integrals int(0)^(pi/2)sin2xtan^(-1)(sinx)dx

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  12. Evaluate the definite integrals int(0)^(pi)(xtanx)/(secx+tanx)dx

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  13. Evaluate the definite integrals int(1)^(4)[abs(x-1)+abs(x-2)+abs(x-3...

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  14. Evaluate the following definite integrals : int(1)^(3)(dx)/(x^(2)(x+...

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  15. Prove the following int(0)^(1)xe^(x)dx=1

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  16. Prove the following int(-1)^(1)x^(17)cos^(4)xdx=0

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  17. Prove the following overset((pi)/(2)) underset(0) int sin^(3)xdx=(2...

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  18. Prove the following overset((pi)/(4)) underset(0) int 2 tan^(3)x dx...

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  19. Prove the following overset(1)underset(0)int sin^(-1)x dx=(pi)/(2)-...

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  20. Evaluate int(0)^(1)e^(2-3x)dx as a limit of a sum.

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