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

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

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int(x^(2)+1)/(xsqrt(x^(2)+2x-1)sqrt(1-x^(2)-x))dx`
`=int(1+(1)/(x^(2)))/(sqrt(x+2-(1)/(x))sqrt((1)/(x)-x-1))dx`
`"Let "t=sqrt(x+2-(1)/(x))`
`therefore" "dt=(1)/(2sqrt(x+2-(1)/(x)))(1+(1)/(x^(2)))dx`
`therefore" "I=int(2dt)/(sqrt(1-t^(2)))`
`=2sin^(-1)t+c`
`=2sin^(-1)sqrt(x-(1)/(x)+2)+c`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Subjective Type|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Comprehension Type|2 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|1 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

int_(1)^(2)x^(2)dx is equal to

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

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

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

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

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

The value of sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)] is equal to

int e^(sin^(-1)x)((log_(e)x)/(sqrt(1-x^(2)))+(1)/(x))dx is equal to

int x.2^(ln(x^(2)+1))dx is equal to