Please solve the following

Asked by Balbir | 6th Oct, 2017, 12:07: PM

Expert Answer:

begin mathsize 16px style integral fraction numerator dx over denominator open parentheses sinx space minus space 2 cosx close parentheses open parentheses 2 sinx space plus space cosx close parentheses end fraction
integral fraction numerator dx over denominator 2 sin squared straight x space minus space 2 cos squared straight x space minus space 3 sinx space cosx end fraction
Dividing space by space cos squared straight x space to space numerator space and space denominator comma
integral fraction numerator begin display style fraction numerator 1 over denominator cos squared straight x end fraction end style dx over denominator begin display style fraction numerator 2 sin squared straight x over denominator cos squared straight x end fraction end style space minus begin display style fraction numerator space 2 cos squared over denominator cos squared straight x end fraction end style minus begin display style fraction numerator space 3 sinx space cosx over denominator cos squared straight x end fraction end style end fraction
integral fraction numerator sec squared straight x space dx over denominator 2 tan squared straight x space minus space 2 space minus space 3 tanx end fraction
Put space tanx space equals space straight t
rightwards double arrow sec squared xdx space equals space dt
integral fraction numerator dt over denominator 2 straight t squared space minus space 2 space minus space 3 straight t end fraction
1 half integral fraction numerator dt over denominator straight t squared minus begin display style fraction numerator 3 straight t over denominator 2 end fraction end style minus 1 end fraction
Using space completing space square space method space you space can space solve space this space further.
end style

Answered by Sneha shidid | 22nd Dec, 2017, 09:41: AM