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

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

A

`(pi)/2 log2`

B

`pilog2`

C

`log2`

D

`(pi)/8 log 2`

Text Solution

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The correct Answer is:
D
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TARGET PUBLICATION-DEFINITE INTEGRALS-COMPETITIVE THINKING
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  2. int0^(pi/2) (xsinxcosx)/(cos^4x+sin^4x) dx=

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

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  4. The value of int(8 log(1+x))/(1+x^(2)) dx is

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  5. int(0)^(pi)[cotx]dx, where [.] denotes the greatest integer function, ...

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  6. int2^8 sqrt(10-x)/(sqrtx+sqrt(10-x))dx

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  7. int(2016)^(2017)(sqrt(x))/(sqrt(x)+sqrt(4033-x))dx is equal to

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  8. int(pi//4)^(3pi//4)(dx)/(1+cosx) is equal to

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  9. The integral int2^4(logx^2)/(logx^2+log(36-12 x+x^2)dx is equal to:...

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  10. The value of int(-pi//2)^(pi//2)(1)/(e^(sinx)+1) dx is equal to

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  11. The value of overset(sqrt("In"3))underset(sqrt("In"2))int(xsinx^(2))/(...

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  12. The value of the integral I = int(1//2014)^(2014)(tan^(-1) x)/x dx is

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  13. The value of the definite integral 1/pi int(pi/2)^((5pi)/2) e^(tan^(-...

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  14. If f(x)=f(pi+e-x) and inte^pif(x)dx=2/(e+pi), then inte^pi xf(x)dx is ...

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  15. The value of int(pi//4)^(3pi//4)(phi)/(1+sinphi)d phi is

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  16. Let I(1) =int(a)^(pi-a)xf(sinx)dx,I(2)=int(a)^(pi-a)f(sinx)dx, then I(...

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  17. If f(x)=(e^(2))/(1+e^(x)),I(1)=overset(f(a))underset(f(-a))int xg{x(1-...

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

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  19. int0^pi x f(sin x)dx is equal to

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  20. If I(1)=int(0)^(pi//2)f(sin2x)sin x dx and I(2)=int(0)^(pi//4)f(cos2x)...

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