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CBSE Class 12-science Answered

Integration sin2x dx/( sin4 x  cos4 x)
Asked by haroonrashidgkp | 11 Nov, 2018, 03:57: PM
answered-by-expert Expert Answer
begin mathsize 16px style If space the space question space which space you space have space posted space like space this straight I equals integral fraction numerator sin 2 straight x over denominator sin to the power of 4 straight x plus cos to the power of 4 straight x end fraction dx straight I equals integral fraction numerator 2 sinxcosxdx over denominator sin to the power of 4 straight x plus cos to the power of 4 straight x end fraction straight I equals integral fraction numerator 2 sinxcosxsec to the power of 4 xdx over denominator open parentheses sin to the power of 4 straight x plus cos to the power of 4 straight x close parentheses sec to the power of 4 straight x end fraction straight I equals integral fraction numerator 2 tanxsec squared straight x over denominator 1 plus tan to the power of 4 straight x end fraction dx Put space tanx equals straight t rightwards double arrow sec squared xdx equals dt straight I equals integral fraction numerator 2 tdt over denominator 1 plus straight t to the power of 4 end fraction straight t squared equals straight z rightwards double arrow 2 tdt equals dz straight I equals integral fraction numerator dz over denominator 1 plus straight z squared end fraction straight I equals tan to the power of negative 1 end exponent straight z plus straight c straight I equals tan to the power of negative 1 end exponent left parenthesis straight t squared right parenthesis plus straight c straight I equals tan to the power of negative 1 end exponent left parenthesis tan squared straight x right parenthesis plus straight c end style
Answered by Sneha shidid | 12 Nov, 2018, 11:06: AM

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