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int(1+cos4x)/(cotx-tanx)dx...

`int(1+cos4x)/(cotx-tanx)dx`

A

`A=(1)/(8),BinR`

B

`A=-(1)/(8),B inR`

C

`A=(1)/(4),BinR`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
We have , `I=int(1+cos 4x)/(cotx-tanx)dx`
`rArrI=int(2cos^(2)2x sinx cosx)/(cos^(2)x-sin^(2)x)=intsin2x cos2x dx`
`rArrI=(1)/(2)intsin 4x dx =-(1)/(8)cos4x +B`
Hence , `A=-(1)/(8)andBinR`
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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Solved Example
  1. Evaluate: int("log"(x+sqrt(1+x^2)))/(sqrt(1+x^2))dxdot

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  2. The value of int(sqrt(1+x))/(x)dx , is

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  3. int(1+cos4x)/(cotx-tanx)dx

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  4. Evaluate: int(x^7)/((1-x^2)^5)\ dx .

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

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  6. The value of int(dx)/(x^n(1+x^n)^(1/ n)) is equal to

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  7. If int(cosx-sinx)/(sqrt(8-sin2x))dx=sin^(-1)((sinx+cosx)/(a))+C then...

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  8. Evaluate int(3x^(2)"tan"(1)/(x)-x"sec"^(2)(1)/(x))dx.

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  9. If intx log (1+(1)/(x))dx =f(x).log(e)(x+1)+g(x)log(e)x+Lx+C , t...

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  10. int(e^((x^(2)+4Inx))-x^(3)e^(x^(2)))/(x-1)dx equals to

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

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  12. int(1)/((x-1)sqrt(x^(2)-1))dx equals

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  13. intsqrt(x-3)(sin^(-1)(Inx)+cos^(-1)(Inx))dx is equal to

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  14. int(1-x^(7))/(x(1+x^(7)))dx equals

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  15. Evaluate: (sin^3x dx)/((cos^4x+3cos^2x+1)tan^(-1)(secx+cosx)

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  16. int((x-x^5)^(1//5))/(x^6)dx is equal to :

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  17. int(tanx)/(sqrt(sin^(4)x+cos^(4)x))dx is equal to

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  18. If intsqrt((cos^(3)x)/(sin^(11)x))dx =-2(Atan^(-9/2)+Btan^(-5/2)x) + C...

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  19. int ((f (x) g' (x) -f' (x) g (x))/(f (x) g(x)))(log (g(x )) - log (f(x...

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  20. int ((f (x) g' (x) -f' (x) g (x))/(f (x) g(x)))(log (g(x )) - log (f(x...

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