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Evaluate the following integrals : int...

Evaluate the following integrals :
`int(tan^(-1)x)` dx.

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The correct Answer is:
`(pi^(2)-4pi)/(16)+logsqrt(2)`
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ARIHANT PUBLICATION-INTEGRATION -PART V (QUESTIONS FOR PRACTICE) (4 MARK)
  1. Evaluate the following integrals : int(pi//3)^(pi//2)(sqrt((1+cosx))...

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  2. Evaluate the following integrals : int(0)^(pi//4)(dx)/(cos^(3)xsqrt(...

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  3. Evaluate the following integrals : int(0)^(1//sqrt(2))(sin^(-1)x)/((...

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  4. Evaluate the following integrals : int(tan^(-1)x) dx.

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  5. Evaluate the following integrals : int(0)^(1)x^(5)(4-x^(2))dx.

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  6. Evaluate the following integrals : int(0)^(1)x^(7)sqrt((1+x^(2))/(1-...

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  7. Evaluate the following integrals : int(0)^(a)x^(2)(a^(2)-x^(2))dx

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  8. If f is an even function and int(-2)^(0)f(t)dt=(3)/(2), then find int(...

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  9. int(0)^(2)(x-[x])dx, where [x] is the greatest integer of x.

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  10. Evaluate the following integrals : int(-1)^(2){|x|+[x]}dx

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  11. Evaluate the following integrals : int(0)^(1)2x(1-x)^(n)dx.

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  12. Evaluate the following integrals : int(0)^(2)xsqrt(2-x)dx.

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  13. Evaluate the following integrals : int(0)^(pi//2)(tan^(7)x)/(cot^(7)...

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  14. Evaluate the following integrals : int(0)^(pi//2)(dx)/(1+sqrt(tanx))

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  15. Evaluate the following integrals : int(0)^(pi//2)log|(4+3sinx)/(4+3c...

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  16. Evaluate the following integrals : int(0)^(1)log|(1)/(x)-1|dx.

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  17. Evaluate the following integrals : int(0)^(pi//2)(sinx-cosx)/(1+sinx...

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  18. Evaluate the following integrals : int(0)^(1)tan^(-1)((2x-1)/(1+x-x^...

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  19. Evaluate the following integrals : int(0)^(1)cot^(-1){1-x+x^(2)}dx.

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  20. Show that int(0)^(pi)log|tanx|dx=0.

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