∫ x^2/根号（4-x^2）dx

来源：百度知道 编辑：UC知道 时间：2024/05/09 14:18:59
具体步骤

>> sym x;
>> simple(int(x^2/sqrt(4-x^2),x))

simplify:

-1/2*x*(4-x^2)^(1/2)+2*asin(1/2*x)

radsimp:

-1/2*x*(4-x^2)^(1/2)+2*asin(1/2*x)

combine(trig):

-1/2*x*(4-x^2)^(1/2)+2*asin(1/2*x)

factor:

-1/2*x*(-(x-2)*(x+2))^(1/2)+2*asin(1/2*x)

expand:

-1/2*x*(4-x^2)^(1/2)+2*asin(1/2*x)

combine:

-1/2*x*(4-x^2)^(1/2)+2*asin(1/2*x)

convert(exp):

-1/2*x*(4-x^2)^(1/2)+2*asin(1/2*x)

convert(sincos):

-1/2*x*(4-x^2)^(1/2)+2*asin(1/2*x)

convert(tan):

-1/2*x*(4-x^2)^(1/2)+2*asin(1/2*x)

collect(x):

-1/2*x*(4-x^2)^(1/2)+2*asin(1/2*x)

mwcos2sin:

-1/2*x*(4-x^2)^(1/2)+2*asin(1/2*x)

ans =

-1/2*x*(4-x^2)^(1/2)+2*asin(1/2*x)

ans即为答案.

a=√(4-x^2) dx/da=a/√(4-a^2)

∫(4-a^2)/a*a/√(4-a^2)da
=∫√