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Find int[sqrt(cotx)+sqrt(tanx)]dx...

Find `int[sqrt(cotx)+sqrt(tanx)]dx`

A

`sqrt(2)log(sqrt(tanx)-sqrt(cotx))+C`

B

`sqrt(2)log|sinx+cosx+sqrt(sin2x)|+C`

C

`sqrt(2)log|sinx-cosx+sqrt(2)sinx cosx|+C`

D

`sqrt(2)log|sin(x+pi//4)+sqrt(2)sinx cosx|+C`

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int(cosx-sinx)/(sqrt(cosx sinx))dx`
Put `sinx+cosx=t, " so that " 2sinx cosx=t^(2)-1`
` :. I=sqrt(2)int(dt)/(sqrt(t^(2)-1))=sqrt(2)log|t+sqrt(t^(2)-1)|+C`
`=sqrt(2)log|sinx+cosx+sqrt(sin2x)|+C`
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CENGAGE-INDEFINITE INTEGRATION-Exercise (Single)
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  3. Find int[sqrt(cotx)+sqrt(tanx)]dx

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  4. If I= int (sin 2x)/((3+4cosx)^(3))dx, then I equals

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  5. int(ln((x-1)/(x+1)))/(x^2-1)dxi se q u a lto 1/2(ln((x-1)/(x+1)))^2+...

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  6. int sqrt(e^(x)-1)dx is equal to

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  7. int sqrt((x^(2)+1)/(x^(2)(1-x^(2))))dx=

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  8. int(sqrt(x^2+10 x+24))/(x+5)dx is equal to

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  9. The value of int(1+logx)/(sqrt((x^(x))^(2)-1))dx " is "

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  10. If intx^5(1+x^3)^(2/3)dx=A(1+x^3)^(8/3)+B(1+x^3)^(5/3)+C ,then A) A=1...

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  11. int(sin2x)/(sin^4x+cos^4x)dxi se q u a lto cot^(-1)(tan^2x)+c tan^...

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  12. int(x+2)/((x^2+3x+3)sqrt(x+1))dx is equal to 1/3tan^(-1)(x/(sqrt(3(x+1...

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  13. int(sec xdx)/(sqrt(sin(2x+A)+sinA)) " is equal to "

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  14. int(cos2x)/((e^(-x)+cosx)sqrt(1+sin2x))dx,x in(0,(pi)/(2)) is equal t...

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  15. "If " int(cos 4x+1)/(cotx-tanx)dx=Acos4x+B, " then "

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  16. If int(dx)/(x^2(x^n+1)^((n-1)/n))=-(f(x))^(1/n)+C then f(x) is (...

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  17. int sqrt((cosx-cos^3x)/(1-cos^(3) x)dx is equal to Option A: 2/3 si...

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  18. intx((lna^(x/2)/(3a^((5x)/2)b^(3x))+(lnb^b^x)/(2a^(2x)b^(4x)))dx(w h e...

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  19. int(3+2cosx)/((2+3cosx)^2)dxi se q u a lto ((sinx)/(3cosx+2))+c (b) ...

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  20. "If " (d)/(dx)f(x)=f'(x), " then " int(xf'(x)-2f(x))/(sqrt(x^(4)f(x)))...

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