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CBSE Class 12-science Answered

integration dx/(sin4 x + cos4x)
Asked by haroonrashidgkp | 11 Nov, 2018, 03:57: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral fraction numerator dx 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 sec to the power of 4 xdx over denominator tan to the power of 4 straight x plus 1 end fraction Put space tanx equals straight t sec squared xdx equals dt straight I equals integral fraction numerator left parenthesis 1 plus tan squared straight x right parenthesis sec squared xdx over denominator tan to the power of 4 straight x plus 1 end fraction straight I equals integral fraction numerator open parentheses 1 plus straight t squared close parentheses dt over denominator straight t to the power of 4 plus 1 end fraction straight I equals integral fraction numerator open parentheses begin display style 1 over straight t squared end style plus 1 close parentheses over denominator open parentheses straight t minus begin display style 1 over straight t end style close parentheses squared plus 2 end fraction dt Put space straight t minus 1 over straight t equals straight u open parentheses 1 over straight t squared plus 1 close parentheses dt equals du straight I equals integral fraction numerator du over denominator straight u squared plus 2 end fraction straight I equals fraction numerator 1 over denominator square root of 2 end fraction tan to the power of negative 1 end exponent open parentheses fraction numerator straight u over denominator square root of 2 end fraction close parentheses plus straight c straight I equals fraction numerator 1 over denominator square root of 2 end fraction tan to the power of negative 1 end exponent open parentheses fraction numerator straight t minus 1 over straight t over denominator square root of 2 end fraction close parentheses plus straight c straight I equals fraction numerator 1 over denominator square root of 2 end fraction tan to the power of negative 1 end exponent open parentheses fraction numerator tan straight x minus 1 over tanx over denominator square root of 2 end fraction close parentheses plus straight c straight I equals fraction numerator 1 over denominator square root of 2 end fraction tan to the power of negative 1 end exponent open parentheses fraction numerator tanx minus cotx over denominator square root of 2 end fraction close parentheses plus straight c end style
Answered by Sneha shidid | 13 Nov, 2018, 09:28: AM

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