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int(sin2x)/(sin^4x+cos^4x)d x...

`int(sin2x)/(sin^4x+cos^4x)d x`

A

`cot^(-1)(tan^(2)x)+c `

B

`tan^(-1)(tan^(2)x)+c `

C

`cot^(-1)(cot^(2)x)+c `

D

`tan^(-1)(cot^(2)x)+c `

Text Solution

Verified by Experts

The correct Answer is:
B
` I= int(sin2x)/(sin^(4)x+cos^(4)x)dx`
`=int(2sinx cosx)/(sin^(4)x+cos^(4)x)dx`
`=int(2tanx sec^(2)x)/(1+tan^(4)x)dx `
`"Let " tan^(2)x=t " or " 2tanxsec^(2)xdx=dt`
` :. I=int(dt)/(1+t^(2))=tan^(-1)t+C=tan^(-1)(tan^(2)x)+C`
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CENGAGE ENGLISH-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
  1. The value of int(1+logx)/(sqrt((x^(x))^(2)-1))dx " is "

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  2. "If "int x^(5)(1+x^(3))^(2//3)dx=A(1+x^(3))^(8//3)+B(1+x^(3))^(5//3)+c...

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  3. int(sin2x)/(sin^4x+cos^4x)d x

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

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  5. Evaluate the following Integrals : int (sec x .dx)/(sqrt(sin (x+2A...

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  6. int(cos2x)/((e^(-x)+cosx)sqrt(1+sin2x))dx,x in(0,(pi)/(2)) is equal t...

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  7. int(cos4x-1)/(cotx-tanx)dx is equal to

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  8. If int(dx)/(x^2(x^n+1)^((n-1)/n))=-(f(x))^(1/n)+C then f(x) is (...

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  9. int sqrt((cosx-cos^3x)/(1-cos^3x))dx is equal to

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  10. intx((lna^(x/2)/(3a^((5x)/2)b^(3x))+(lnb^b^x)/(2a^(2x)b^(4x)))dx(w h e...

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  11. int(3+2cosx)/((2+3cosx)^2)dx is equal to (a) ((sinx)/(3cosx+2))+c (b...

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  12. "If " (d)/(dx)f(x)=f'(x), " then " int(xf'(x)-2f(x))/(sqrt(x^(4)f(x)))...

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  13. The value of the integral int((1-costheta)^(2/7))/((1+costheta)^(9/7))...

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  14. If int(dx)/(sqrt(sin^(3)xcos^(5)x))=a sqrt(cot x)+bsqrt(tan^(3)x)+c, t...

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  15. "I f"int(dx)/(cos^3xsqrt(sin2x))=a(tan^2x+b)sqrt(tanx)+c

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  16. If int(dx)/((x+2)(x^(2)+1)) = alog|1+x^(2)|+btan^(-1)x+ 1/5log|x+2|+C,...

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  17. Ifint(3e^x-5e^(-x))/(4e^x+5e^(-x))dx=a x+bln(4e^x+5e^(-x))+C ,t h e n ...

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  18. If intf(x)sinxcosxdx=1/(2(b^2-a^2))lnf(x)+c ,then f(x) is equal to

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  19. int(x^(9))/((4x^(2)+ 1)^(6))dx is equal to

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  20. If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b , th...

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