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Asked by mohdomerdon 7th March 2019, 3:00 PM
Answered by Expert
Answer:
begin mathsize 12px style I space equals space integral fraction numerator x plus 1 over denominator x squared plus 3 x plus 12 end fraction d x space equals space 1 half integral fraction numerator 2 x plus 3 minus 1 over denominator x squared plus 3 x plus 12 end fraction d x
I space equals space 1 half integral fraction numerator 2 x plus 3 over denominator x squared plus 3 x plus 12 end fraction d x space minus 1 half integral fraction numerator d x over denominator x squared plus 3 x plus 12 end fraction
I space equals space 1 half integral fraction numerator 2 x plus 3 over denominator x squared plus 3 x plus 12 end fraction d x space minus 1 half integral fraction numerator d x over denominator open parentheses x plus begin display style 3 over 2 end style close parentheses squared plus open parentheses 12 minus begin display style 9 over 4 end style close parentheses end fraction
I space equals space 1 half integral fraction numerator 2 x plus 3 over denominator x squared plus 3 x plus 12 end fraction d x space minus 1 half integral fraction numerator d x over denominator open parentheses x plus begin display style 3 over 2 end style close parentheses squared plus open parentheses begin display style fraction numerator square root of 49 over denominator 2 end fraction end style close parentheses squared end fraction
I space equals space log open parentheses square root of x squared plus 3 x plus 12 end root close parentheses space minus fraction numerator 1 over denominator square root of 49 end fraction tan to the power of negative 1 end exponent open parentheses fraction numerator 2 x plus 3 over denominator square root of 49 end fraction close parentheses plus C
end style
Answered by Expert 7th March 2019, 5:22 PM
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