Integral{x^7/x^2+1}

Asked by rraj.15266 | 5th Nov, 2017, 10:45: PM

Expert Answer:

begin mathsize 16px style integral fraction numerator straight x to the power of 7 over denominator straight x squared plus 1 end fraction dx
straight x squared plus 1 space equals space straight t rightwards double arrow straight x squared equals straight t minus 1
2 xdx equals dt rightwards double arrow xdx equals dt over 2
integral fraction numerator straight x to the power of 6 space xdx over denominator straight x squared plus 1 end fraction
integral fraction numerator begin display style open parentheses straight x squared close parentheses cubed end style over denominator straight x squared plus 1 end fraction xdx
integral fraction numerator begin display style open parentheses straight t minus 1 close parentheses cubed end style over denominator straight t end fraction cross times dt over 2
1 half integral fraction numerator straight t cubed minus 3 straight t squared plus 3 straight t minus 1 over denominator straight t end fraction dt
1 half integral open parentheses straight t cubed over straight t minus fraction numerator 3 straight t squared over denominator straight t end fraction plus fraction numerator 3 straight t over denominator straight t end fraction minus 1 over straight t close parentheses dt
1 half integral open parentheses straight t squared minus 3 straight t plus 3 minus fraction numerator begin display style 1 end style over denominator begin display style straight t end style end fraction close parentheses dt
Now space you space can space integrate space further.
end style

Answered by Sneha shidid | 11th Dec, 2017, 02:23: PM