Home
Class 12
MATHS
int(dx)/((1+sqrt(x))sqrt((x-x^(2)))) is ...

`int(dx)/((1+sqrt(x))sqrt((x-x^(2))))` is equal to

A

`2(sqrt((x)/sqrt(1-x))-(1)/(sqrt(1-x)))+c`

B

`2(sqrt((x)/sqrt(1-x))-(1)/(1-x))+c`

C

`2(sqrt((x)/(1-x))-(1)/(sqrt(1-x)))+c`

D

`2(sqrt((x)/(1-x))-(1)/(1-x))+c`

Text Solution

Verified by Experts

The correct Answer is:
C
`Let int(1)/((1+sqrtx)sqrt(x-1))dx`
Putting `x=sin^(2)t and dx=2 sin t cos t dt,` we get
`I=int(2sint cos tdt)/((1+sint)sqrt(sin^(2)t-sin^(4)t))`
`rArr" "I=2int(1)/(1+sin t)dt=2int(1-sint)/(cos^(2)t)dt`
`=2int(sec^(2)t-sect tan t)dt`
`=2(tan t-sec t)+c`
`rArr" "2(sqrt((x)/(1-x))-(1)/(sqrt(1-x)))+c`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Subjective Type|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Archives JEE ADVANCED (Single Correct Answer Type)|1 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

int(dx)/((1-x)sqrt(x))

int (dx)/(sqrt(x)-1)

int (dx)/(sqrt(x)+sqrt(x-2))

The value of int_(0)^(1)(xdx)/((x+sqrt(1-x^(2)))sqrt(1-x^(2))) is equal to -

int dx/((1+sqrtx)sqrt(x-x^2) is equal to ?

int(dx)/sqrt(2x-x^2) is equal to

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

int(dx)/(sqrt(x+3)-sqrt(x+2))

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

int(dx)/((1-x^(2))sqrt(1-x^(2)))