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int0^(pi//2)(cosx)/((2+sinx)(1+sinx))dx ...

`int_0^(pi//2)(cosx)/((2+sinx)(1+sinx))dx` equals (a)`log(2/3)` (b) `log(3/2)` (c) `log(3/4)` (d) `log(4/3)`

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Verified by Experts

Given,
`int_0^(pi)/2 (cosxdx)/((1+sinx)(2+sinx))`
let `sinxdx=t`
`cosxdx=dt`
when,
`x=0,t=0` and when `x=pi/2,1` ...
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. If int0^pi 1/(a+bcosx)dx=pi/sqrt(a^2-b^2), then int0^pi 1/(a+bcosx)^2d...

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  2. int0^1sqrt((1-x)/(1+x))dx= (pi)/2 (b) (pi)/2-1 (c) (pi)/2+1 (d) ...

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  3. int0^(pi//2)(cosx)/((2+sinx)(1+sinx))dx equals (a)log(2/3) (b) l...

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  4. int0^pi(xtanx)/(secx+cosx)dxi s (pi^2)/4 (b) (pi^2)/2 (c) (3pi^2)/2...

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  5. int0^2 1/(1+tanx)dx is equal to (pi^)/4 (b) (pi^)/3 (c) (pi^)/2 ...

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  6. int(-pi//2)^(pi//2)"sin"|x|dx is equal to 1 (b) 2 (c) -1 (d) ...

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  7. The value of the integral int0^oox/((1+x)(1+x^2))dx is (pi)/2 (b) ...

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  8. int0^3(3x+1)/(x^2+9)dx = (pi)/(12)+log(2sqrt(2)) (b) (pi)/2+log(2sqr...

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  9. I10=int0^(pi/2)x^(10)sinx dx then I10+90I8 is (A) 10(pi/2)^6 (B) 10(p...

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  10. Evaluate:int0^(pi//2)(cosx)/(1+cosx+sinx)dx

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  11. Evaluate: int0^(pi//2)1/(3+2cosx)dx

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  12. Evaluate: int(pi//4)^(pi//2)cos2xlogsinxdx

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  13. integrate int0^(2pi) e^x . sin (pi/4 + x/2) dx

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  14. Evaluate: int0^1(2x)/(5x^2+1)dx

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  15. Evaluate:(i) int0^(pi//6)(2+3x^2)dx

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  16. Evaluate: (i)int0^4 1/(x+sqrt(x))dx (ii) int0^1(2x)/(5x^2+1)dx

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  17. Evaluate the following definite integrals (1-58): int1^2 1/(sqrt((x...

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  18. If (x) is of the form f(x)=a+b x+c x^2, show that int0^1f(x)d...

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  19. Evaluate: int0^oo1/((x^2+a^2)(x^2+b^2))dxdot

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  20. Evaluate the following integrals: int0^(pi//6)cos^(-3)2thetasin2th...

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