Home
Class 12
MATHS
The value of the integral int(x^2+x)(x^(...

The value of the integral `int(x^2+x)(x^(-8)+2x^(-9))^(1/(10))dx` is `5/(11)(x^2+2x)^((11)/(10))+c` (b) `5/6(x+1x)^((11)/(10))+c` `6/7(x+1)^((11)/(10))+c` (d) none of these

A

`(5)/(11)(x^(2)+2x)^(11//10)+c`

B

`(5)/(6)(x+1)^(11//10)+c`

C

`(6)/(7)(x+1)^(11//10)+c`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Given that
`I=int(x^(2)+x)(x^(-8)+2x^(-9))^(1//10) dx`
`=int (x+1)(x^(2)+2x)^(1//10)dx`
Now put `x^(2)+2x=t " and "(x+1)dx=(dt)/(2)`
` :. I=int t^(1//10)(dt)/(2)=(1)/(2)xx(10)/(11)t^(11//10)+C=(5)/(11)t^(11//10)+C`
` =(5)/(11)(x^(2)+2x)^(11//10)+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 the integral int(x^(2)+x)(x^(-8)+2x^(-9))^((1)/(10))dx(5)/(11)(x^(2)+2x)^((11)/(10))+c( b) (5)/(6)(x+1x)^((11)/(10))+c(6)/(7)(x+1)^((11)/(10))+c( d) none of these

Let f(x)=int(x^(2)dx)/((1+x^(2))(1+sqrt(x^(2)+1))) and f(0)=0 Then value of f(1) will be (7)/(11)(tan(theta)/(2))_((11)/(7))^((11)/(7))+C (b) (7)/(11)((cos theta)/(2))^((11)/(7))+C(7)/(11)(s int h(eta)/(2))^((11)/(7))+C (d)none of these

intdx/(x(1+x^10))= (A) 1/10 log((1+x^10)/x^10)+c (B) 1/10 log(x^10/(1+x^10))+c (C) 1/(1+x^10)^2+c (D) none of these

The value of the integral I=int(2x^(9)+x^(10))/((x^(2)+x^(3))^(3))dx is equal to (where, C is the constant of integration)

If (1)/(9!)+(1)/(10!)=(x)/(11!) then x=

3x-(y+7)/(11)+2=10 and 2y+(x+11)/(7)=10

If (1)/(3)+(1)/(2)+(1)/(x)=4, then x=?(5)/(18)(b)(6)/(19) (c) (18)/(5)(d)(24)/(11)

If (x-1)/(x)=3, then the value of 1+(1)/(x^(2)) is (a) 9(b) 10(c)11 (d) None of these

The value of int x^(5)(x^(10)+x^(5)+1)(2x^(10)+3x^(5)+6)^(1/5)dx is (A) (1)/(6)(2x^(10)+3x^(5)+6)^(1/5)+c (B) (1)/(36)(2x^(15)+3x^(10)+6x^(5))^(6/5)+c (C) (1)/(36)(2x^(15)+3x^(10)+6x^(5))^(11/5)+c (D) x^(15)+3x^(10)+(x^(5))/(5)+c

The solution set of the inequality log_(10)(x^(2)-16)<=log_(10)(4x-11) is 4,oo) (b) (4,5)(c)((11)/(4),oo)(d)((11)/(4),5)