x的平方乘以(根号里a^2-x^2)的原函数是多少

此题用换元积分法令：x=a sint,t属于（-π/2。π/2）则dx=acostdt原式：∫x^2√(a^2-x^2)dx=∫a^2 (sint)^2 * acost * acostdt=a^4∫(sint)^2 * (cost)^2 dt=(a^4)/4∫(sin2t)^2 dt=(a^4)/8∫(1-cos4t)dt=(a^4)/8[∫dt-∫cos4tdt]=(a^4)/8[t-1/4 sin4t]再把t换回来,太难得编辑了,分数又少,从略,