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`int(1+x+sqrt(x+x^2))/(sqrt(x)+sqrt(1+x))dxi se q u a lto` `1/2sqrt(1+x)C` (b) `2/3(1+x)^(x/2)+C` `sqrt(1+x)+c` (d) `3/2(1+x)^(3/2)+C`

A

`(1)/(2)sqrt(1+x)+C`

B

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

C

`sqrt(1+x)+C`

D

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

Text Solution

Verified by Experts

The correct Answer is:
b
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OBJECTIVE RD SHARMA-INDEFINITE INTEGRALS-Exercise
  1. If x^2!=n pi-1, n in N. Then, the value of int x sqrt((2sin(x^2+1)-sin...

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  2. Given f(x) =|{:(0,x^(2)-sinx,cosx-2),(sinx-x^(2),0,1-2x),(2-cosx,2x-1,...

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  3. int(1)/(x^(1//2)(1+x^(2))^(5//4))dx is equal to

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  4. int(x^(2))/((a+bx^(2))^(5//2))dx is equal to

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  5. int(sin^(3)x)/((1+cos^(2)x)sqrt(1+cos^(2)x+cos^(2)x+cos^(4))x)dx is eq...

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  6. int(1)/(sqrt(sin^(3)xsin(x+alpha)))dx is equal to

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  7. The antiderivative of (3^(x))/(sqrt(1-9^(x))) with respect to x is

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  8. Integration of (1)/(sqrt(x^(2)=9)) with respect to (x^(2)+1) is equa...

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  9. If int(sintheta-costheta)/((sintheta+costheta)sqrt(sinthetacostheta+s...

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  10. The primitive of the function f (x) =(2x+1)|cosx|, when (pi)/(2)ltxl...

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  11. The primitive of the function f (x) = (2x+1) |sinx|, where piltxlt2p...

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  12. Let intsqrt((5-x)/(2+x))dx equal

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  13. The value of the integral int(xsin x^(2)e^(secx^(2)))/(cos^(2)x^(2))dx...

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

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  15. Evaluate: int(e^(2x)-2e^x)/(e^(2x)+1)dx

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  16. int(1)/(cosx-sinx)dx is equal to

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  17. int(a^(x//2))/(sqrt(a^(-2)-a^(x)))dx is equal to

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  18. int(f'(x))/(f(x)log{f(x)})dx=

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  19. int(e^x)/((1+e^x)(2+e^x))dx

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  20. int(1+x+sqrt(x+x^2))/(sqrt(x)+sqrt(1+x))dxi se q u a lto 1/2sqrt(1+x)...

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