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int((x-x^5)^(1//5))/(x^6)dx is equal to ...

`int((x-x^5)^(1//5))/(x^6)dx` is equal to :

A

`(5)/(24)((1)/(x^(4))-1)^(6//5)+C`

B

`(5)/(24)(1-(1)/(x^(4)))^(6//5)+C`

C

`-(5)/(24)(1-(1)/(x^(4)))^(6//5)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let `I=int((x-x^(5))^(1//5))/(x^(6))dx=int((1)/(x^(4))-1)^(1//5)(1)/(x^(5))dx`
`rArrI=-(1)/(4)int((1)/(x^(4))-1)^(1//5)((-4)/(x^(5)))dx=-((1)/(x^())-1)^(1//5)d((1)/(x^(4))-1)`
`rArr I=-(5)/(24)((1)/(x^(4))-1)^(6//5)+C`
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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Solved Example
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  2. Evaluate: (sin^3x dx)/((cos^4x+3cos^2x+1)tan^(-1)(secx+cosx)

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  5. If intsqrt((cos^(3)x)/(sin^(11)x))dx =-2(Atan^(-9/2)+Btan^(-5/2)x) + C...

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  7. int ((f (x) g' (x) -f' (x) g (x))/(f (x) g(x)))(log (g(x )) - log (f(x...

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  9. Let the equation of a curve passing through the point (0,1) be given b...

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  10. Evaluate: int1/(sin^4x+cos^4x)dx

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  11. Evaluate the following Integrals : int (sec x .dx)/(sqrt(sin (x+2A...

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  12. "Let "int e^(x){f(x)-f'(x)}dx=phi(x). " Then "int e^(x) f(x)dx " is "

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  13. Evaluate "if " int(1)/(x+x^(5))dx=f(x)+c," then " int(x^(4))/(x+x^(5...

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  14. If intf(x)dx=F(x), then int x^(3)f(x^(2))dx is equal to

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  15. If n is an odd positive integer, then int|x^(n)|dx is equal to

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  16. If inte^(ax)cosbx dx=(e^(2x))/(29)f(x)+C , then f'' (x)=

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  17. int(sin^(4)x)/(sin^(4)x+cos^(4)x)dx is equal to

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  18. If intf(x)dx=2 {f(x)}^(3)+C , then f (x) is

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  19. Let g (x) be a differentiable function satisfying (d)/(dx){g(x)}=g(x)...

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  20. If intg(x)dx=g(x), then the value of the integral intf(x)g(x){f(x)+2...

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