Home
Class 12
MATHS
If int(1-x^(7))/(x(1+x^(7)))dx=alog(e)|x...

If `int(1-x^(7))/(x(1+x^(7)))dx=alog_(e)|x|+blog_(e)|x^(7)+1|+c,` then

A

`a=1`

B

`a= -1`

C

`b=(2)/(7)`

D

`b= -(2)/(7)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
`I=int(1-x^(7))/(x(1+x^(7)))dx=a log_(e)|x|+b log_(e)|1+x^(7)|+c`
Differentiating both sides w.r.t. x, we get
`(1-x^(7))/(x(1+x^(7)))=(a)/(x)+b.(7x^(6))/(1+x^(7))`
`implies1-x^(7)=a(1+x^(7))+7bx^(7)`
`impliesa=1, a+7b= -1`
`implies b= -2//7`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Comprehension)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Matrix)|4 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Single)|77 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)/(x)ln((x)/(e^(x)))dx=

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

int(e^(x))/(e^(x)+1)dx= ……………

int(e^(x)+1)/(e^(x))dx :

If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2logg(x)+C , then

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

Evaluate int(1)/(1+e^(x))dx

int_(1)^(2)(1/(x)-(1)/(2x^(2)))e^(2x)dx

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

Evaluate 1 int (x^(7))/(x + 1) dx