设f(sinx)=x/sin^2 x 求∫f(x)dx
2个回答

let

x =siny

∫f(x)dx

=∫f(siny)d(siny)

= ∫ [y/(siny)^2] d(siny)

=-∫ y d[1/(siny)]

= -y/siny + ∫ (1/siny) dy

=-y/siny + ln|cscy-coty| + C

= -arcsin(x)/x + ln| 1/x - √(1-x^2)/x | + C

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