Home
Class 12
MATHS
The value of int (dx)/((1+sqrtx)(sqrt(x-...

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

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
Let `I=int(dx)/((1+sqrt(x))sqrt((x-x^(2))))`
If `sqrt(x)=sinp, " then " (1)/(2sqrt(x))dx=cos p dp`
` :. I=int (2sin p cos p dp)/((1+sinp)sinp cosp)`
`=2int (dp)/((1+sin p))`
`=2int((1-sinp)dp)/(cos^(2)p)`
`=2{int sec^(2)p dp-int(tanp sec p)dp}`
`=2(tanp-secp)+C`
`=2(sqrt((x)/((1-x)))-(1)/(sqrt((1-x))))+C=(2(sqrt(x)-1))/(sqrt((1-x)))+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Comprehension)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.9|15 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

The value of int(dx)/((1+sqrt(x))(sqrt(x-x^(2)))) is equal to

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

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

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

int(1)/(sqrt(9x-4x^(2)))dx is equal to

The value of int(dx)/(x+sqrt(a^(2)-x^(2))) , is equal to

The value of int(1)/((2x-1)sqrt(x^(2)-x))dx is equal to (where c is the constant of integration)

int(1)/(sqrt(8+2x-x^(2)))dx is equal to

The value of int(dx)/(x(sqrt(1-x^(3)))) is equal to