Home
Class 12
MATHS
Evalaute: int(x-1)/((x+1)sqrt(x^(3)+x^(2...

Evalaute: `int(x-1)/((x+1)sqrt(x^(3)+x^(2)+x)`dx

Text Solution

Verified by Experts

`rArr I=int(x^(2)-1)/((x+1)^(2)sqrt(x^(3)+x^(2)+x))dx` [Muliplying the `N^(')` and `D^(') by (x+1)]`
`I=int(x^(2)-1)/((x^(2)+2x+1)sqrt(x^(3)+x^(2)+x))` dx
`rArr I=int(1/x^(2))/((x^(2)+2x+1)sqrt(x^(3)+x^(2)+x))`dx
`rArr I = int(1-1/x^(2))/(x+1/x+2)(sqrt(x+1/x+1))dx` (Dividing `N^(')` and `D^(')` by `(x+1)]`
`rArr I=2tan^(-1)sqrt(x+1/x+1+C)`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    RESONANCE|Exercise EXERCISE -1 SUBJECTIVE QUESTIONS|1 Videos

  • INDEFINITE INTEGRATION

    RESONANCE|Exercise SUBJECTIVE QUESTIONS|14 Videos

  • GEOMETRY

    RESONANCE|Exercise Exercise-1 (Part-I: Previous Asked Question For Pre RMO)|50 Videos

  • MATRICES & DETERMINANT

    RESONANCE|Exercise HLP|33 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int(1)/((x-1)sqrt(2x+3))dx

int(dx)/(x sqrt(1-x^(3)))=

int(dx)/(x sqrt(1-x^(3)))=

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

int(dx)/((x+3)sqrt(x+1))

int_1^2 (x-1)/(x+1). 1/sqrt(x^3+x^2+x)dx

Evaluate: int1/(x^(3)sqrt(x^2-1))\ dx

int(dx)/((1+x)sqrt(3+2x-x^(2)))=

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

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