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Find the following integrals : (c ) in...

Find the following integrals :
(c ) `int cos^(5) x sqrt( sin x) dx`,

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Verified by Experts

The correct Answer is:
(c ) `((2)/(3) - (2)/( 7) sin^(2) x+ (2)/(11) sin^(4) x) sqrt( sin^(3) x) +C`;
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IA MARON-INDEFINITE INTEGRALS, BASIC METHODS OF INTEGRATION-4.2. Integration by Substitution
  1. I= int ( x^2 + 3) /( sqrt ( 2x -5)^(3) ) dx.

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  2. Evaluate: int(x^2-1)/((x^4+3x^2+1)tan^(-1)(x+1/x))dx

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  3. I= int ( sqrt( alpha^(2) - x^(2) ) )/( x^4) dx.

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  4. I= int ( dx)/( a^(2) sin^(2) x + b^(2) cos^(2) x) .

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  5. I= int root(3) ( 1+ 3 sin x) cos x dx.

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  6. I= int ( sin x dx)/( sqrt( cos x) ).

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  7. I= int ( dx)/( ("arc" cos x)^(5) sqrt(1-x^2) ).

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  8. I= int ( x^2 + 1) /( root( 3) ( x^(3) + 3x + 1) )d x.

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  9. I= int ( sin 2 x)/( 1+ sin^(2) x) dx.

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  10. I= int ( 1+ "In" x)/( 3+ x "In" x) dx.

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  11. Evaluate the following integrals : (a) int ( root( 3) (1+ "In" x) )/...

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  12. Evaluate the following integrals : (b) int ( dx)/( x "In" x) ,

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  13. Evaluate the following integrals : (c ) int ( xdx)/( sqrt( 3-x^4) ),

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  14. Evaluate the following integrals : (d) int ( x^( n-1) )/( x^( 2n) + ...

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  15. What is int (sin sqrtx)/(sqrtx) dx equal to ?

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  16. Evaluate the following integrals : int ("In" x + (1)/( "In" x) ) (dx...

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  17. Find the following integrals : (a) int x^(2) root( 3) ( 1-x) dx,

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  18. Find the following integrals : (b) int ("In" x dx)/( x sqrt (1+ "In"...

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  19. Find the following integrals : (c ) int cos^(5) x sqrt( sin x) dx,

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  20. Find the following integrals : (d) int ( x^5)/( sqrt( 1-x^2) ) dx.

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