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int0^oolog(x+1/x)(dx)/(1+x^2)...

`int_0^oolog(x+1/x)(dx)/(1+x^2)`

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Verified by Experts

`pi ln 2`
`int_{0}^{infty} log (x+frac{1}{x}) frac{1}{1+x^{2}} d x`
Substitute `x=tan theta`
`Rightarrow d x=sec ^{2} theta d theta`
...
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. int0^(pi//2)sin2xlogtanx\ dx\ is equal to pi//2 b. pi c. 0 d. 2pi

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  2. The value of int0^pi1/(5+3cosx)dx is pi//2 b. pi//4 c. 0 d. pi//8

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  3. int0^oolog(x+1/x)(dx)/(1+x^2)

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  4. int0^(2a)f(x)dx is equal to 2int0^af(x)dx b. 0 c. int0^af(x)dx+int0^...

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  5. If f(a+b-x)=f(x),\ t h e n\ inta^b xf(x)dx is equal to (a+b)/2inta^bf(...

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  6. The value of int0^1tan^(-1)((2x-1)/(1+x-x^2))dx ,\ is 1 b. -1 c. 0 d....

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  7. Choose the correct answer The value of int0pi/2log((4+3sinx)/(4+3cosx)...

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  8. The value of int(pi//2)^(pi//2)(x^3+x\ cos x+tan^5x+1)dx , is 2 b. pi ...

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  9. Evaluate the following integral: int0^4x\ sqrt(4-x)\ dx

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  10. Evaluate the following integral: int1^5x/(sqrt(2x-1))dx

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  11. Evaluate the following integral: int0^1tan^(-1)x\ dx

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  12. Evaluate the following integral: int0^1tan^(-1)((2x)/(1-x^2))dx

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  13. Evaluate the following integral: int0^1(1-x)/(1+x)dx

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  14. Evaluate the following integral: int0^(pi//2)(sin^2x)/((1+cos x)^2)dx

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  15. Evaluate the following integral: int0^(pi//2)(cos x)/(1+sin^2x)dx

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  16. Evaluate the following integrals: int0^1sqrt((1-x)/(1+x))dx

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  17. Evaluate the following integral: int0^(pi//4)cos^4xsin^3x\ dx

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  18. Evaluate the following integral: int0^(pi//2)x^2cos2x\ dx

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  19. Evaluate the following integral: int2^4(x^2+x)/(sqrt(2x+1))dx

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  20. int0^1(cos^(- 1)x)^2dx

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