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The value of int(sin^(2)xcos^(2)x)/((sin...

The value of `int(sin^(2)xcos^(2)x)/((sin^(3)x+cos^(3)x)^(2))dx` , is

A

`(1)/(3(1+tan^(3)x))`

B

`-(1)/(3(1+tan^(3)x))`

C

`(1)/(1+tan^(3)x)`

D

`-(1)/(1+tan^(3)x)`

Text Solution

Verified by Experts

The correct Answer is:
B
We have , `I=int(sin^(2)xcos^(2)x)/((sin^(3)x+cos^(3)x)^(2))dx`
`rArrI=int(tan^(2)xsec^(2)x)/((1+tan^(3)x)^(2))dx ["Dividing"N^(r)and D^(r) " by "cos^(6)x]`
`rArr I=(1)/(3)int(3tan^(2)x sec^(2)x)/((1+tan^(3)x)^(2))dx`
`rArr I=(1)/(3)int(1)/((1+tan^(3)x)^(2))d(1+tan^(3)x)`
`=-(1)/(3(1+tan^(3)x))+C`
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OBJECTIVE RD SHARMA-INDEFINITE INTEGRALS-Solved Example
  1. int(1+x-x^(- 1))e^(x+x^(- 1))dx=

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  2. If In=int( lnx)^n dx then In+nI(n-1)

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  3. The value of int(sin^(2)xcos^(2)x)/((sin^(3)x+cos^(3)x)^(2))dx , is

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  4. The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitr...

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  5. If f(x) =int (x^2+sin^2x)/(1+x^2) sex^2x dx and f(0) =0 then f(1) =

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  6. At present, a firm is manufacturing 2000 items. It is estimated tha...

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  7. If int f(x)dx=psi(x), then int x^5f(x^3)dx

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  8. The integral int(1+x-1/x)e^(x+1/x)dx is equal to

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  9. if int(1-5sin^2x)/(cos^5xsin^2x)dx=f(x)/(cos^5x)+c then f(x)

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  10. int(x^(7m)+x^(2m)+x^m)(2x^(6m)+7x^m+14)^(1/m)dx

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

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

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  13. The integral int(1+x-1/x)e^(x+1/x)dx is equal to

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  14. int e^(x^4) (x + x^3 +2x^5) e^(x^2) dx is equal to

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  15. int[sin(101 x)*sin^(99)x]dx

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  16. Suppose int(1-7cos^2x)/(sin^7xcos^2x)dx=(g(x))/(sin^7x)+c where C is a...

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  17. int(x^(2)+x)(x^(-8)+2x^(-9))^(1//10)dx is equal to

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  18. If int 2/(2-x)^2 ((2-x)/(2+x))^(1//3)\ dx = lambda ((2+x)/(2-x))^mu + ...

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  19. Let f(x) be a quadratic function such that f(0)=1 and int(f(x))/(x^2(x...

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

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