怎样用初等行变换把一次函数化为二次函数
发布网友
发布时间：2024-10-23 22:58
共1个回答
热心网友
时间：2024-11-06 05:39
∫x arcsinx dx
= (1/2) ∫ arcsinx dx^2
= (1/2)x^2 arcsinx - (1/2) ∫ x^2 ( 1/(1-x^2)^(1/2) ) dx
let x = sina
dx = cosa da
∫ x^2 ( 1/(1-x^2)^(1/2) ) dx
= ∫ (sina)^2 da
= ∫ (1-cos2a)/2 da
= a/2 - sin2a/4
= arcsinx/2 + x(1-x^2)^(1/2)/2
therefore
∫x arcsinx dx
= (1/2)x^2 arcsinx - (1/2) ∫ x^2 ( 1/(1-x^2)^(1/2) ) dx
= (1/2)x^2 arcsinx - (arcsinx)/ 4 -x(1-x^2)^(1/2)/4 +C
