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int(1+tan^2x)/(1-tan^2x)dx...

`int(1+tan^2x)/(1-tan^2x)dx`

A

`log ((1-tanx)/(1+tanx))+c`

B

`log ((1+tanx)/(1-tanx))+c`

C

`(1)/(2) log ((1-tanx)/(1+tanx))+c`

D

`(1)/(2) log ((1+tanx)/(1-tanx))+c`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `l=int(1+tan^(2)x)/(1-tan^(2)x)dx`
`=int(sec^(2)x)/(1-tan^(2)x)dx`
Put `tanx=timpliessec^(2)xdx=dt`
`:.l=int(dt)/(1-t^(2))=(1)/(2xx1)log""((1+t)/(1-t))+c`
`=(1)/(2)log((1+tanx)/(1-tanx))+c`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 07-PAPER 2( MATHEMATICS)
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  2. int{log(logx)+(1)/((logx)^(2))}dx=x {f (x)-g(x)}+C, then

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  3. int(1+tan^2x)/(1-tan^2x)dx

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  4. The area (in sq unit) of the triangle formed by x+y+1=0 and the pair o...

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  5. The equation y^(2)-x^(2)+2x-1=0, represents

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  6. The value of the integral int f(0)^(2)|x^(2)-1|dx is

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  7. If AB=I and B=A', then

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  8. If the system of equations 2x-3y+5z=12, 3x+y+lambdaz= mux7+y+8z=17 ha...

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  9. The differential equation of all parabolas whose axis are parallel ...

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  10. If (x^2+y^2)dy=xydx and y(1)=1 and y(xo)=e, then xo=

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  11. The integrating factor of x(dy)/(dx)+(1+x)y=x is

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  12. if 0<=x<=pi and 81^(sin^2x)+81^(cos^2x)=30 then x=

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  13. In Delta ABC , a= 6 ,b=3 and cos (A-B) = 4/5 .Then are of triangle i...

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  14. Find the equation of a normal to the curve y = x loge x which is paral...

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  15. Area common to the circle x^(2)+y^(2)=9 an the parbola y^(2)=8x is

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  16. If three points A, B and C have position vectors hati + x hatj + 3 ha...

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  17. If a,b,c are mutually perpendicular unit vectors then |a+b+c|=

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  18. In a Boolean Algebra pvvp is equl to

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  19. If P be the point (2,6, 3) then the equation of the plane through P, a...

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  20. सिद्ध कीजिए की f(x)=tan ^(-1)(sin x + cos x ),x gt 0 से प्रदत फलन f...

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