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Prove the following int(1)^(3)(dx)/(x^...

Prove the following
`int_(1)^(3)(dx)/(x^(2)(x+1))=(2)/(3)+"log"(2)/(3)`

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NCERT TAMIL-INTEGRALS-EXERCISE 7.12
  1. Evaluate the definite integrals int(pi/2)^(pi)e^(x)((1-sinx)/(1-cosx...

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

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  3. Evaluate the definite integrals int(0)^((pi)/(2))(cos^(2)xdx)/(cos^...

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  4. Evaluate the definite integrals int((pi)/(6))^((pi)/(3))(sinx+cosx)...

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

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

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

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

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

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  10. Prove the following int(1)^(3)(dx)/(x^(2)(x+1))=(2)/(3)+"log"(2)/(3)

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

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

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

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  14. Prove the following int(0)^(pi/4)2tan^(3)xdx=1-log2

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  15. Prove the following int(0)^(1)sin^(-1)xdx=(pi)/(2)-1

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

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  17. int(dx)/(e^(x)+e^(-x)) is equal to

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  18. Choose the correct answers int(cos2x)/((sinx+cosx)^(2))dx is equal t...

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  19. Choose the correct answers If f (a + b - x) = f (x), then int(a)^(b)...

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  20. Choose the correct answers The value of int(0)^(1)tan^(-1)((2x-1)/(1...

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