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Evaluate the following integral: int0^(p...

Evaluate the following integral: `int_0^(pi//2)1/(1+tanx)`

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`int_0^(pi//2)1/(1+tanx)`
`=int_0^(pi//2) frac{1}{1+tan(pi/2 -x)}dx`
`int_0^(pi//2) frac{tan x}{1+tanx}dx`
`=pi/4`
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Prove that: int0^(pi//2)logsinx\ dx=\ int0^(pi//2)logcosx\ dx=-pi/2log...

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  2. Evaluate: int0^pilog(1+cosx)dx

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  3. Evaluate the following integral: int0^(pi//2)1/(1+tanx)

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  4. Evaluate the following integral: int0^(pi//2)(sqrt(cotx))/(sqrt(cotx\ ...

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  5. Evaluate the following integral: int0^a1/(x+sqrt(a^2-x^2))dx

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  6. Evaluate the following integral: int0^(pi//2)1/(1+cotx)dx

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  7. Evaluate the following integral: int0^(pi//2)(sin^(3//2)\ )/(sin^(3//2...

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  8. Evaluate the following integral: int0^(pi//2)1/(1+tanx)dx

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  9. Evaluate the following integral: int0^oo(logx)/(1+x^2)dx

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  10. Evaluate the following integral:int0^1("log"(1+x))/(1+x^2)dx

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  11. Evaluate the following integral:int0^pi(xtanx)/(secx\ cos e c\ x)dx

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  12. Evaluate the following integral:int0^pixsin^3x\ dx

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  13. Evaluate the following integral:int0^pi(xsinx)/(1+sinx)dx

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  14. Evaluate the following integral:int0^(pi//2)(tan^7x)/(tan^7x+cot^7x)dx

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  15. Evaluate the following integral:int0^(pi//2)x\ s in xcos^2x\ dx

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  16. Evaluate the following integral:int(-pi//2)^(pi//2)sin^3x\ dx

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  17. Evaluate the following integral:int(-1)^1log((2-x)/(2+x))dx\

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  18. Evaluate the following integral:int0^pilog(1-cos x)dx

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  19. Evaluate the following integral:int(-pi)^pi(2x(1+sinx))/(1+cos^2dx)dx

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  20. Evaluate the following integral:int0^2x\ sqrt(2-x)\ dx

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