Question

Вычислить интеграл {dx/sqrt 1-9x^2

Answer 1

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

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

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