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int(0)^(oo)(x logx)/((1+x^(2))^(2)) dx=...

`int_(0)^(oo)(x logx)/((1+x^(2))^(2)) dx=`

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int_(0)^(oo)(dx)/((1+x^(2))^(4))=

int_(1)^(3)(logx)/((1+x)^(2))dx

I=int_(0)^(oo)(x)/((x^(2)+a^(2))^(2))dx

int_(0)^(oo)(log(1+x^(2)))/(1+x^(2))dx=

The value of int_(0)^(oo)(logx)/(a^(2)+x^(2))dx is

" 8."int_(0)^(oo)(log x)/(1+x^(2))dx

int_(0)^(oo)(x)/((1+x)(1+x^(2)))dx

A DAS GUPTA-Properties and Application of definite Integrals-EXERCISE
  1. Prove that: int0^(pi//2)logsinx\ dx=\ int0^(pi//2)logcosx\ dx=-pi/2log...

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  2. int(0)^(pi//2)log(tanx+cotx)dx=pi(log2)

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  3. int(0)^(oo)(x logx)/((1+x^(2))^(2)) dx=

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  4. int(pi//6)^(pi//3)(1)/((1+sqrt(tanx)))dx=(pi)/(12)

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  5. Q. int0^pi(e^(cos^2x)( cos^3(2n+1) x dx, n in I

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  6. int(0)^(2pi) (sin 2 theta)/(a-b cos 2 theta )d theta =

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  7. Evaluate int0^1 log(1+x)/(1+x^2)dx

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  8. Prove that: y=int(1/8)^(sin^2x)sin^(-1)sqrt(t)dt+int(1/8)^(cos^2x)cos^...

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  9. Evaluate the following: int0^(pi/2) |cosx-sinx|dx

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  10. Evaluate the following:int-2^2(|x|+|x-1|)dx

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  11. Prove that inta^b{[x]+[-x]}dx=a-b,where [x]is the greatest integer lex...

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  12. Statement-I int0^9[sqrtx]dx=13, Statement-II int0^(n^2) [sqrt x]dx=(n(...

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  13. Show that: int0^x[x]dx=[x]([x]-1)/2+[x](x-[x]), where [x] denotes the ...

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  14. The value of the integral overset(100pi)underset(0)int sqrt(1-cos2x)" ...

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  15. Evaluate the following : int(0)^(pi)(dx)/(1+sinx)

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  16. Evaluate the following:int0^(10pi)|cosx|dx

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  17. Evaluate int(0)^(npi+t)(|cosx|+|sinx|)dx, where n epsilonN and t epsil...

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  18. Show that: inta^bf(x)dx=int(a+c)^(b+c)f(x-c)dx and hence show that int...

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  19. If f(x) is a continuous function defined on [0,\ 2a]dot\ Then prove t...

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  20. If f(t) is an odd function, then varphi(x)=inta^xf(t)dx is an even fun...

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