Question
Thu April 17, 2014 By: Saisri Akondi

 

integration of sin^2x cos^2x/(sin^3x+cos^3x)^2dx                                                                                                                                                                                                                                                                                                                                   options:   1. sin^3x/1+cos^3x +c           2.1/1+cot^3x   +c       3. -cos^3x/3(1+sin^3x)  +c                        4.-1/3(1+tan^3x) +c

 

 

 

 

 

 

Expert Reply
Wed April 23, 2014
integral subscript blank superscript blank fraction numerator sin squared x cos squared x over denominator open parentheses sin cubed x plus cos cubed x close parentheses squared end fraction d x  equals integral subscript blank superscript blank fraction numerator sin squared x cos squared x over denominator cos to the power of 6 x open parentheses begin display style fraction numerator sin cubed x over denominator cos cubed x end fraction end style plus 1 close parentheses squared end fraction d x  equals integral fraction numerator tan squared x s e c squared x over denominator open parentheses tan cubed x plus 1 close parentheses squared end fraction d x  N o w space t a k i n g space t equals 1 plus tan cubed x rightwards double arrow d t equals 3 tan squared x s e c squared x d x  equals integral 1 over t squared d t  equals minus 1 over t plus c  equals minus fraction numerator 1 over denominator 1 plus tan cubed x end fraction plus c
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