Question

Вычислить интеграл {dx/sqrt 1-9x^2

Answer 1

$intlimits {dfrac{dx}{sqrt{1 - 9x^{2}}}} = intlimits {dfrac{dx}{sqrt{9 bigg(dfrac{1}{9} - x^{2} bigg)}}} = intlimits {dfrac{dx}{ sqrt{9}sqrt {bigg(dfrac{1}{9} - x^{2} bigg)}}}} =$

$=dfrac{1}{sqrt{9}} cdotp intlimits {dfrac{dx}{sqrt{dfrac{1}{9} - x^{2} }}} = dfrac{1}{3} cdotp arcsin bigg(dfrac{x}{sqrt{dfrac{1}{9} } } bigg) =dfrac{arscin 3x}{3} =$

$= dfrac{arscin 3x}{3} + C, C in R.$