计算∫36x^3÷√62-41x^2dx的不定积主要步骤F2

336x的不定积分；dx主要内容本文根据分部积分法、三角换元法以及凑分法等方法,36x介绍不定积分的计算步骤1=dx―2也2-41x※由分子分母的关系，变形化简使用凑分法求得:36x62-41x2dx2232f xdx+i41^62-41x241J62-41x236fx62-41x2-62x]dx41J62-4•f x^/62-41x2d x-1116*£d62-41x22J62-41x2=-1^62-41x2d62-41x2-2232*^/62-41x2,1_________1_______=12*^/621417一2232*乔*^621417+07※利用不定积分的分部积分方法x2*xdx18x2d62-41x21=36^62-41x247^62-41x2_____[o____-_^/x2d^/62-41x218-77X2y162-41S+石/-\y62-41x,dx2,41[g__________1_______----------212yj62-41x23+c41X62-41x-12*77141二一五x2^62-41x2-18^62-41x2d62-41x2,※利用三角函数的代换关系，进行三角还原积分,621______设乂二7而s int,贝1J cost=^j\/62-41x2,此时:gee rrzI sin3tdA/jysint2232/62_141y41J^62-62s in2t，s inatcostdt2232^/^=36*第2Jsin3tdt,进一步化简有Js int1-cos2t dt,2232a口4122232沂,r

2.fs intdt—-—fs intcos tdt,2232a_2232M病2232=~412cost+cos2tdeost,412412_2232M距2232cost+cos3t+c,413*412_______[_________________2232y62-41x2+162-41x23+c.二一4r‘。