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int(sin^(3)x)/((1+cos^(2)x)sqrt(1+cos^(2...

`int(sin^(3)x)/((1+cos^(2)x)sqrt(1+cos^(2)x+cos^(4))x)dx` is equal to

A

`sec^(-1)(secx+cosx)+C`

B

`sec^(-1)(secx-cosx)+C`

C

`sec^(-1)(secx-tanx)+C`

D

none of these

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Verified by Experts

The correct Answer is:
a
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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Exercise
  1. Let x^(2)ne pi-1, n in N, then intxsqrt((2sin(x^(2)+1)-sin2(x^(2)+1)...

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  2. Given, f(x)=|(0, x^(2)-sin x, cos x-2),(sin x-x^(2),0,1-2x),(2-cos x,2...

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

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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)|sin x|, when pi lt x lt 2 p...

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  12. IfI=intsqrt((5-x)/(2+x))dx ,t h e nIe q u a l sqrt(x+2)sqrt(5+x)+3si...

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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. Evaluate: int(x^2-1)/(xsqrt((x^2+alphax+1)(x^2+betax+1)))dx

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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 is equal to

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  19. Evaluate: 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))dx is equal to

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