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Prove that : int0^pi (xtanx)/(secxcosecx...

Prove that : `int_0^pi (xtanx)/(secxcosecx)dx =pi^2/4`.

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MODERN PUBLICATION-INTEGRALS-EXERCISE
  1. Evaluate: underset(0)overset(pi//2)int log tan x dx

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  2. Evaluate the following integrals: int(3ax)/(b^2+c^2x^2)dx

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

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  4. Evaluate the following integrals: int(x^2)/(x^4+x^2+1)dx

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  5. Evaluate the following integrals: int(sqrt(1+x^2))/(x^4)dx

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  6. Evaluate the following integrals: int(sin^-1x)/((1-x^2)^(1//2))dx

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  7. Evaluate the following integrals : int(sin^(6)x+cos^(6)x)/(sin^(2)xcos...

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  8. Find: int(sqrtx)/(sqrt(a^3-x^3))

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  9. Evaluate the following integrals: underset(pi//3)overset(pi//2)intsq...

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  10. Evaluate the following integrals: underset(-pi//4)overset(pi//4)int ...

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  11. Evaluate the following integrals: underset(0)overset(pi//2)int(tanx)...

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  12. Evaluate the following integrals: int e^(x) (tanx+1)sec xdx

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  13. Evaluate the following integrals: int 1/(x^(2)-9)dx

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  14. Evaluate: underset(e ) overset(e^2)int(dx)/(xlogx)

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  15. Evaluate int x^(2) log x dx.

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  16. Evaluate : int1^4 (3x^2+2x)dx as the limit of sum.

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  17. Evaluate: underset(0)overset(pi)int(xsinx)/(1+cos^2x)dx

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  18. Prove that : int0^pi (xtanx)/(secxcosecx)dx =pi^2/4.

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  19. Evaluate int(2 sin2x-cos x)/(6-cos^ (2)x-4sinx) dx.

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  20. By using the properties of definite integrals, evaluate the integral: ...

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