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Evaluate: int(sin2x)/(sin^4x+cos^4x)dx...

Evaluate: `int(sin2x)/(sin^4x+cos^4x)dx`

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 PUBLICATION-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. Evaluate: int(sin2x)/(sin^4x+cos^4x)dx

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

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

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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. I=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^(a^(x/2))/(3a^((5x)/2)b^(3x))+(lnb^(b^x))/(2a^(2x)b^(4x)))dx(...

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

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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^3xcos^5x))=asqrt(cotx)+bsqrt(tan^3)x+c , then a=-...

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  15. Ifint(dx)/(cos^3xsqrt(sin2x))=a(tan^2x+b)sqrt(tanx)+c ,t h e n a=(sq...

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  16. Evaluate: int dx/( (x + 2)(x^2 + 1) )

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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^(5))/((4x^(2)+ 1)^(4))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 ,t h...

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