1、介绍通过分部积分法、三角换元法以及凑分法等方法，计算不定积分的详细过程与步骤。
2、解法一：思路：根据分子分母的关系，直接变形化简使用凑分法求得：
I=-∫(89/49)[x(64-49x^2)-64x]dx/√(64-49x^2)
=-(89/49)∫x(64-49x^2)dx/√(64-49x^2)+ (5696/49)∫xdx/√(64-49x^2)
=-(89/49)∫x√(64-49x^2)dx-(2848/1)*1/49^2∫d(64-49x^2)/√(64-49x^2)
=-89 *1/49^2∫√(64-49x^2)d(64-49x^2)- 5696*1/49^2√(64-49x^2)
=(178/3) *1/49^2√(64-49x^2)^3-5696*1/49^2*√(64-49x^2)+c
3、解法二：思路：利用不定积分的分部积分方法求得：
I=89∫x^2*xdx/√(64-49x^2)
=-(89/98)∫x^2d(64-49x^2)/√(64-49x^2)
=-(89/98)∫x^2d√(64-49x^2)=-(89/98)x^2√(64-49x^2)+(89/98) ∫√(64-49x^2)dx^2
=-(89/98)x^2√(64-49x^2)-(89/2)*1/49^2∫√(64-49x^2)d(64-49x^2)
=-(89/98)x^2√(64-49x^2)-(89/3)*1/49^2√(64-49x^2)^3+c
4、解法三：
思路：利用三角函数的代换关系，进行三角换元积分求得。
设x=√(64/49)sint，则cost=(1/√64)√(64-49x^2),此时：
I=(5696/49)*√(64/49)∫sin^3td[√(64/49)sint]/√(64-64sin^2t),
=89*(64/49)^2∫sin^3tcostdt/√64*cost,
=(5696√64 /49^2)∫sin^3tdt,
5、=(5696√64 /49^2)∫sint(1-cos^2 t)dt
=(5696√64 /49^2)∫sintdt-(5696√64 /49^2)∫sintcos^2 tdt
=-(5696√64 /49^2)cost+(5696√64 /49^2)∫cos^2tdcost=-(5696√64 /49^2)cost+(5696√64 /3*49^2)cos^3t+c
=-(5696/49^2)√(64-49x^2)+(89/3)*(1/49^2)√(64-49x^2)^3+c.
