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CBSE Class 12-science Answered

<p>&nbsp;</p> <p style="margin: 0px; padding: 0px; line-height: 1.3em; border: 0px; outline: 0px; vertical-align: baseline; background-color: transparent; display: inline !important;"><strong>integration of sin^2x cos^2x/(sin^3x+cos^3x)^2dx &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; options: &nbsp; 1. sin^3x/1+cos^3x +c &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 2.1/1+cot^3x &nbsp; +c &nbsp; &nbsp; &nbsp; 3. -cos^3x/3(1+sin^3x) &nbsp;+c &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;4.-1/3(1+tan^3x) +c</strong></p> <p style="margin: 0px; padding: 0px; line-height: 1.3em; border: 0px; outline: 0px; vertical-align: baseline; background-color: transparent; display: inline !important;">&nbsp;</p> <p style="margin: 0px; padding: 0px; line-height: 1.3em; border: 0px; outline: 0px; vertical-align: baseline; background-color: transparent; display: inline !important;">&nbsp;</p> <p style="margin: 0px; padding: 0px; line-height: 1.3em; border: 0px; outline: 0px; vertical-align: baseline; background-color: transparent; display: inline !important;">&nbsp;</p> <p style="margin: 0px; padding: 0px; line-height: 1.3em; border: 0px; outline: 0px; vertical-align: baseline; background-color: transparent; display: inline !important;">&nbsp;</p> <p style="margin: 0px; padding: 0px; line-height: 1.3em; border: 0px; outline: 0px; vertical-align: baseline; background-color: transparent; display: inline !important;">&nbsp;</p> <p style="margin: 0px; padding: 0px; line-height: 1.3em; border: 0px; outline: 0px; vertical-align: baseline; background-color: transparent; display: inline !important;">&nbsp;</p>
Asked by Saisri Akondi | 17 Apr, 2014, 04:23: PM
Expert Answer
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
Answered by | 23 Apr, 2014, 02:28: PM
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