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Let f(x)=int(x^(2)dx)/((1+x^(2))(1+sqrt(...

Let `f(x)=int(x^(2)dx)/((1+x^(2))(1+sqrt(1+x^(2))))and f(0)=0.`
`f(1)` is

A

`log_(e)(1+sqrt(2))`

B

`log_(e)(1+sqrt(2))-pi/4`

C

`log_(e)(1+sqrt(2))+pi/4`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
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ARIHANT MATHS-INDEFINITE INTEGRAL -Exercise (Single Option Correct Type Questions)
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  3. If int f(x)dx=F(x), then intx^3f(x^2)dx is equal to :

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  4. If n is a positive integer, then find int x^n dx

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  5. Let F(x) be the primitive of (3x+2)/(sqrt(x-9)) w.r.t. x. If F(10)=60...

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  6. int[sin (ax+b) cos(ax+b)]dx is equal to

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  7. The value of int x log x (log x - 1) dx is equal to

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

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  9. Let f(x) be a polynomial satisfying f(0)=2 , f'(0)=3 and f''(x)=f(x) t...

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  10. Find int(x^4 + x^2)dx

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  11. int tan^(4)x dx = A tan^(3) x+ B tan x + f(x), then

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  12. If the anti derivative of int sin^4x/x dx is f(x) then int(sin^4(p+q)...

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  13. Prove that : sin(9-theta\)=cos(81+theta)

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  14. For x^2nenpi+1, n inN(the set of natural numbers), the integral intxsq...

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  15. int(dx)/(cos(2x)cos(4x))=

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  16. int(1-7cos^(2)x)/(sin^(7)xcos^(2)x)dx=(f(x))/((sinx)^(7))+C, then f(x)...

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  17. Evaluate int(sin^(3)xdx)/((cos^(4)x+3cos^(2)x+1)tan^(-1)(secx+cosx)).

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  18. The primitive of the function f(x)= x | cos x|, when pi/2 lt x lt pi i...

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  19. The primitive of the function f(x)=(2x+1)|sin x|, when pi lt x lt 2 p...

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  20. int (cosx+sinx) dx is equal to :

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