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intdx/(cosx-sinx) is equal to...

`intdx/(cosx-sinx)` is equal to

A

`1/sqrt(2)log|tan(x/2-(3x)/8)|+C`

B

`1/sqrt(2)log|cot(x/2)|+C`

C

`1/sqrt(2)log|tan(x/2-pi/6)|+C`

D

`1/sqrt(2)log|tan(x/2+(3pi)/8)|+C`

Text Solution

Verified by Experts

The correct Answer is:
D
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KC SINHA-INDEFINITE INTEGRALS - FOR COMPETITION-Exercise
  1. (xe^x)/(1+x)^2dx= (A) e^x/(1+x) (B) e^x/(1+x)^2 (C) e^xlog(1+x) (D) no...

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  2. If intsinx/(sin(x-alpha))dx=Ax+Blogsin(x-alpha)+C, then value of (A,B)...

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  3. intdx/(cosx-sinx) is equal to

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  4. If int[(logx-1)/(1+(logx)^2)]^2dx=f(x)/(1+(g(x))^2)+c, then (A) f(x)=x...

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  5. int 1/(cosx+sqrt3sinx) \ dx equals (i) log(tan (x/2+pi/12))+c (ii) l...

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  6. The value of sqrt(2)int(sin"x"dx)/(sin(x-pi/4)) is: (1) x+log|cos(x-pi...

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  7. Ifint(x^4+1)/(x^6+1)dx=tan^(-1)f(x)-2/3tan^(-1)g(x)+C ,t h e n both f...

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  8. int\ (x+1)/(x(1+x \ e^x)^2) \ dx equals

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  9. int(loge(x+1)-logex)/(x(x+1))dx is equal to (A) -1/2[log(x+1)^2-1/2log...

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  10. If int(xe^x)/sqrt(1+e^x)dx=f(x)sqrt(1+e^x)-2logg(x)+c, then

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  11. int(4e^x+6e^(-x))/(9e^x-4e^(-x))dx=A x+Blog(9e^(2x)-4)+C ,t h e n A= ...

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  12. If int[(logx-1)/(1+(logx)^2)]^2dx=f(x)/(1+(g(x))^2)+c, then (A) f(x)=x...

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  13. Statement-1: intdx/(x(1+logx)^2)=-1/(1+logx)+C , Statement-2: int(f(x)...

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  14. Statement-1: int(3-2x)/sqrt(4+2x-x^2)dx=2sqrt(4+2x-x^2)+sin^-1((x-1)/s...

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  15. Statement-1: The function F(x)=intsin^2xdx satisfies F(x+pi)=F(x),AAxi...

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  16. Consider the function F(x)=intx/((x-1)(x^2+1))dxStatement-1: F(x) is d...

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  17. Let a solution y=y(x) of the differential equation xsqrt(x^2-1)dy-ysqr...

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  18. Statement-1: int((x^2+1)/x^2)e^((x^2+1)/x^(2))dx=e^((x^2+1)/x^(2))+C S...

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  19. Statement-1: intsin^-1xdx+intsin^-1sqrt(1-x^2)dx=pi/2x+cStatement-2: s...

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  20. Statement-1: int(sinx)^x(xcotx+logsinx)dx=x(sinx)^xStatement-2: d/dx(f...

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