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If int(x^(5))/(sqrt(1+x^(3)))dx is equa...

If `int(x^(5))/(sqrt(1+x^(3)))dx` is equal to

A

`(2)/(9)(1+x^(3))^(5//2)+(2)/(3)(1+x^(3))^(3//2)+C`

B

`(2)/(9)(1+x^(3))^(3//2)-(2)/(3)(1+x^(3))^(1//2)+C`

C

`log|sqrt(x)+sqrt(1+x^(3))|+C`

D

`x^(2)log(1+x^(3))+C`

Text Solution

Verified by Experts

The correct Answer is:
b
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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Chapter Test
  1. If int(dx)/((x^(2)+1)(x^(2)+4))=k tan^(-1) x + l tan^(-1) . (x)/(2) +C...

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  2. If int log(sqrt(1-x)+sqrt(1+x))dx=xf(x)+Ax+Bsin^(-1)x+C, then

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  3. If int(x^(5))/(sqrt(1+x^(3)))dx is equal to

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  4. The value of : inte^(secx).sec^(3)x(sin^(2)x+cosx+sinx+sinxcosx)dx i...

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  5. If int(2x^(2)+3)/((x^(2)-1)(x^(2)+4))dx=aln((x-1)/(x+1))+btan^(-1).(x)...

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  6. Let f(x)=(x)/((1+x^(n))^(1//n)) for n ge 2 and g(x)=underset("n times"...

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  7. The value of int ((ax^(2)-b)dx)/(xsqrt(c^(2)x^(2)-(ax^(2)+b)^(2))) is ...

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  8. Evalaute: inte^(x)(1+nx^(n-1)-x^(2n))/((1-x^(n))sqrt(1-x^(2n))dx

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  9. int(xcosx+1)/(sqrt(2x^(3)e^(sinx)+x^(2)))dx

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  10. int(x^(3))/((1+x^(2))^(1//3))dx is equal to

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  11. int sinx/sin(x-alpha)dx=Ax+B log (sin(x-alpha))+C then find out (A ,B)

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  12. What is int (x^(2) +1)/(x^(4) - x^(2) + 1) dx equal to ?

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

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  14. int(1+x^(2))/(xsqrt(1+x^(4)))dx is equal to

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  15. int(1+x^(4))/((1-x^(4))^(3//2))dx is equal to

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  16. If int(dx)/(x^(4)+x^(3))= A/x^(2)+B/x+ln|x/(x+1)|+C, then

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  17. If f'(x)=(1)/((1+x^(2))^(3//2)) and f(0)=0, then f(1) is equal to :

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  18. int (x)^(1/3) (root(7)(1+root(3)(x^(4))))dx is equal to

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  19. int(1)/((a^(2)+x^(2))^(3//2))dx is equal to

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  20. int(1)/(x(x^(4)-1))dx is equal to

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