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int\ (sin^2 x cos^2x)/(sin^5x+cos^3xsin...

`int\ (sin^2 x cos^2x)/(sin^5x+cos^3xsin^2x+sin^3xcos^2x+cos^5x)^2 \ dx`

A

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

B

`(1)/( 1 + cot ^(2) x) +C`

C

`(-1)/( 1 + cot ^(3) x ) +C`

D

`(1)/( 1+ cot ^(3) x) +C`

Text Solution

Verified by Experts

The correct Answer is:
A
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DISHA PUBLICATION-INTEGRALS -EXERCISE-2 CONCEPT APPLICATOR
  1. int\ (sin^2 x cos^2x)/(sin^5x+cos^3xsin^2x+sin^3xcos^2x+cos^5x)^2 \ d...

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  2. The value of the limit lim ( n to oo) [(1)/(na) + (1)/( na +1) + (1)...

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  3. Let the equation of a curve passing through the point (0,1) be given b...

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  4. If intf(x)sinxcosx dx=1/(2(b^2-a^2))logf(x)+C, then f(x) is

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  5. If int sqrt2 sqrt (1 + sin x ) dx =- 4 cos (ax +b)+C then the value of...

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  6. Evaluate: int1/(1+3sin^2x+8cos^2x)\ dx

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  7. I = int {log (e) log (e) x + (1)/( (log (e) x ) ^(2))} dx is equal to:

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

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  9. In the integral int(cos 8x+1)/(cot 2x-tan 2x)dx=A cos 8x+k, where k...

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  10. If |x| lt 1" thn "underset(n to oo)"Lt "(1+x)(1+x^(2))(1+x^(4))....(1+...

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  11. int0^1000 e^(x-[x])dx

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  12. Evaluate: ifintf(x)dx=g(x),t h e nintf^(-1)(x)dx

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  13. int(-pi/4) ^(pi/4) (e^theta(thetasintheta))/(e^(2theta)-1)d theta=

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  14. int (x ^(n-1))/( x ^(2n) + a ^(2)) dx =

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  15. If intf(x)cos x dx = 1/2 f^(2)(x)+C, then f(x) can be

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  16. Evaluate: int2^2^x2^2^xdxdot

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  17. The value of int (sqrt ( log 2 )) ^(sqrt( log 3 )) (x sin x ^(2))/( si...

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  18. The value of int((1+x))/(x(1+x e^(x))^(2))dx, is equal to

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  19. The value of int((ax^2-b)dx)/(xsqrt(c^2x^2-(ax^2+b)^2)) is equal to

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  20. int(log sqrt(pi//2))^(log sqrt(pi))e^(2x)sec^(2)((1)/(3)e^(2x))dx=

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  21. Evaluate : int(6x+7)/(sqrt((x-5)(x-4)))\ dx

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