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Integrate the function: (sqrt(x^2+1)[log...

Integrate the function: `(sqrt(x^2+1)[log(x^2+1) - 2logx])/x^4`

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PSEB-INTEGRALS-Exercise
  1. Integrate the function: (x^2+x+1)/((x+1)^2(x+2))

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  2. Integrate the function: tan^(-1)sqrt((1-x)/(1+x))

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  3. Integrate the function: (sqrt(x^2+1)[log(x^2+1) - 2logx])/x^4

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  4. Evaluate the definite integral: int(pi/2)^pi e^x ((1-sinx)/(1-cosx))dx

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  5. Evaluate the definite integral: int0^(pi/4) (sinxcosx)/(cos^4x+sin^4x)...

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  6. Evaluate the definite integral: int0^(pi/2) (cos^2x)/(cos^2x+4sin^2x)d...

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  7. Evaluate the definite integral: int(pi/6)^(pi/3) (sinx+cosx)/(sqrtsin2...

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  8. Evaluate the definite integral: int0^1 (dx)/(sqrt(1+x)-sqrtx)dx

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  9. Evaluate the definite integral: int0^(pi/4) (sinx+cosx)/(9+16sin2x)dx

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  10. Evaluate the definite integral: int0^(pi/2) (sin2xtan^(-1)(sinx))dx

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  11. Evaluate the definite integral: int0^(pi) (xtanx)/(secx+tanx)dx

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  12. Evaluate the definite integral: int1^4 (|x-1|+|x-2|+|x-3|)dx

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  13. int1^3 (dx)/(x^2(x+1)) = (2/3)+log(2/3) ਪ੍ਰਮਾਣਿਤ ਕਰੋ।

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  14. Prove the following: int0^1 (xe^x) = 1

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  15. Prove the following: int-1^1 (x^17cos^4x dx) = 0

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  16. int0^(pi/2) (sin^3x)dx = 2/3 ਪ੍ਰਮਾਣਿਤ ਕਰੋ।

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  17. Prove the following: int0^(pi/4) (2tan^3x)dx = 1-log2

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  18. Prove the following: int0^1 (sin^(-1)x)dx = (pi/2)-1

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  19. Evaluate int0^2 e^(3x) dx as the limit of sums.

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

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