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int(4x^(3))/(1+x^(8)) dx =...

`int(4x^(3))/(1+x^(8)) dx =`

A

`(9x^(4))/(9+x^(9)`

B

`tan^(-1)((x^(4))/(1+x^(8)))`

C

`tan^(-1)x^(4)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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HIMALAYA PUBLICATION-INDEFINITE INTEGRAL-QUESTION BANK
  1. int((1+x)^(2))/(x(1+x^(2)))dx =

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  2. int (1+t^(2))/(1+t^(4))dt =

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  3. int(4x^(3))/(1+x^(8)) dx =

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  4. For the function f(x) = 1+ 3^(x) log 3, the antiderivative F assumes t...

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  5. If an antiderivative of f(x) is e^(x) and that of g(x) is cos x, then ...

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  6. If f(x) = cos x - cos^(2)x + cos^(3)x + …. to oo int f(x) dx =

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  7. If I = int tan^(-1)((2x)/(1-x^(2)))*dx then I-2x*tan^(-1)x =

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  8. int 2/(1-x^(4)) dx = k log ((1+x)/(1-x)) + tan^(-1)x then k =

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  9. int dx/((x^(2)+1)(x^(2)+4))= k tan^(-1) x + l (tan^(-1)) x/2 then

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  10. int dx/(x-x^(3)) = A (log) x^(2)/(1-x^(2)), then A =

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  11. int (sin 2x +cos 2x) dx = 1/sqrt2 sin (2x-a) then a =

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  12. If I(1) = int sin^(-1) x dx and I(2) = int sin^(-1) sqrt(1-x^(2))dx th...

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  13. int d^(2)/(dx^(2))(tan^(-1) x) dx =

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  14. If f(x) = int (x^(2)+sin^(2)x)/(1+x^(2)) sec^(2)x dx and f(0) = 0, the...

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  15. In n (ne 1) in N and I(n) = intcosec^(n) dx then (n-1)((n)+cosec^(n-2)...

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  16. If n(ne 1) in N and I(n) =int sec^(n)x dx then (n-1) I(n)-(n-2)I(n-2) ...

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  17. If n in N and I(n) = intsin^(n) x dx then nI(n)-(n-1)I(n-2) =

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  18. If n in N and I(n) = intcos^(n) xdx then nI(n) - cos^(n-1)x. sinx =

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  19. If n(ne 1) in N and I(n) = int tan^(n) x dx then I(n)+I(n-2) =

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  20. If n(ne 1) in N and I(n) = intcot^(n) x dx then I(n) + (cot^(n-1)x)/(n...

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